From f91f58298397b727f87a5acbfb8bd23925c2db4a Mon Sep 17 00:00:00 2001 From: Silvio Tomatis Date: Fri, 29 May 2026 00:06:05 +0200 Subject: [PATCH 1/7] docs: concept-first README + dictionary-card explainer page Reframe the README around the tententoon idea (same picture, two infinities) rather than implementation: a side-by-side Droste/tententoon visual, a precise one-line definition, the log-polar idea in plain language, and the Escher / de Smit-Lenstra origin. Run and tech details move to a collapsed footer. Add public/explain.html: a standalone 'what is a tententoon' deep-dive styled as an aged-paper dictionary card (syllabified headword, IPA, numbered sense + usage example, bracketed etymology, inline nested-squares SVG mark), flowing into a plain-language account of why the spiral closes seamlessly (the logarithm trick), Escher's hand-drawn blank centre, and the 2003 de Smit-Lenstra completion. Revert the in-app InfoModal copy to the hand-written original and tag it .human-written so it is preserved from future rewrites. Add public/tententoon-demo.gif (spiral demo) for the README + page visuals. docs/screenshots/ holds card previews for this PR. Co-Authored-By: Claude Opus 4.8 --- README.md | 143 ++---- docs/screenshots/dictionary-card-desktop.png | Bin 0 -> 202401 bytes docs/screenshots/dictionary-card-mobile.png | Bin 0 -> 157410 bytes public/explain.html | 504 +++++++++++++++++++ public/tententoon-demo.gif | Bin 0 -> 1129850 bytes src/components/ui1/InfoModal.svelte | 5 +- 6 files changed, 550 insertions(+), 102 deletions(-) create mode 100644 docs/screenshots/dictionary-card-desktop.png create mode 100644 docs/screenshots/dictionary-card-mobile.png create mode 100644 public/explain.html create mode 100644 public/tententoon-demo.gif diff --git a/README.md b/README.md index 3c4b7b4..65d7b21 100644 --- a/README.md +++ b/README.md @@ -1,126 +1,69 @@ -# Tententoon +

tententoon

-> *Een prentententoonstelling.* — M. C. Escher, 1956 +

noun  ·  a self-repeating image whose copies spiral as they shrink — in the manner of M. C. Escher's Print Gallery (1956).

-A browser-native Droste machine. Drop in any photograph, frame the rectangle that should -contain a smaller copy of itself, and watch the image recurse into its own infinity — the -way the boy in Escher's *Print Gallery* stares into the picture he is standing inside of. - -Everything runs locally. No uploads, no backend, no account. Just the canvas, the maths, -and your image. - ---- - -## What it does - -- **Drop or pick** any image — JPEG, PNG, anything the browser can decode. -- **Frame** a rectangle inside it. That rectangle becomes the next iteration of itself. -- **Zoom forever** — a continuous, seamless loop into (or out of) the nested copy. -- **Export** the result as a still PNG, a looping MP4, or a GIF. All produced in-browser. -- **Tweak** the spiral: pick the centre, the scale ratio, the rotation, the depth. -- **Two views**: a polished editor (top bar, tool rail, canvas, inspector, timeline) and a - log-domain explorable for those who like to see the conformal map at work. - -The geometry is the same one Escher's mathematicians used to "complete" the Print Gallery: -a log-polar warp that turns nested similarity into a straight line. We let you see both -sides of that mirror. +

+from the Dutch title Prentententoonstellingprenten (prints) + tentoonstelling (exhibition),
+with the coined word sitting right where the two halves meet.
+A browser tool for making the same move with your own images. +

--- -## Why "Tententoon"? +## Same picture, two infinities -A contraction of *prentententoonstelling* — the Dutch word for "print gallery" — squeezed -the way Escher squeezed his canvas. Short enough to type, long enough to remember. - ---- - -## Run it locally - -```sh -bun install # or: npm install -bun run dev # or: npm run dev -``` + + + + + + + + + +
A photograph of a person holding a frame; inside the frame is the same person holding the same frame, repeating into the distance.The same photograph, with the nested copies rotating as they shrink, winding the whole image into a smooth spiral.
Droste — a picture inside itself, dropping straight down forever.
(this one is a real photograph)
tententoon — the same recursion, bent into a spiral that still closes seamlessly.
-Then open the URL Vite prints. The editor lives at `/`; the log-domain explorable lives -at `/ui1`. +> Same rule — a copy inside a copy inside a copy. One drops straight down; the other takes the scenic route, and still arrives on time. -### Build +## The idea -```sh -bun run build # → dist/ -bun run preview # serve dist/ locally -bun run smoke # headless smoke test -``` +Nest a picture inside itself and you get the **Droste effect**: each copy sits squarely inside the last, shrinking by the same step, forever. ---- +A **tententoon** asks one stranger question — *what if each copy also turns as it shrinks?* The nested frames then wind into a spiral. Straight lines bow into curves, the whole picture twists, and yet nothing tears: follow any line inward and it meets itself exactly. -## How it works, briefly +The trick is a single move — **take the logarithm.** Shrinking-and-repeating is multiplication, and logarithms turn multiplication into addition, so "shrink, then repeat" becomes "slide over, then repeat" — a plain, evenly-spaced grid. Add rotation and that grid simply *tilts*; roll it back up and the tilt is a spiral. The loop is seamless because, in log-space, one full turn is just a shift by exactly one step — landing you on an identical picture. -The Droste effect is a single operation applied to itself: take the outer image rectangle, -map it onto the user's inner rectangle, paint, repeat. After a few iterations the inner -copy is sub-pixel and we stop. +**→ The whole story — why it spirals, and why it never tears:** [silvio-tententoon.pgs.sh/explain.html](https://silvio-tententoon.pgs.sh/explain.html) -For the smooth infinite zoom, the inner rectangle's *scale ratio* `S` and rotation angle -`θ` define a logarithmic spiral. Mapping image coordinates through -`log(z - c) → log(z - c) + log(S) + iθ` turns that spiral into a translation in -log-space — which is why the loop is exactly seamless: translating by one full period -lands on the same picture. +## Where the name comes from -The renderer is WebGL via [twgl.js](https://twgljs.org/), with a CPU fallback worker for -environments without a usable GL context. Supersampling adapts to the local Jacobian so -the spiral's tight centre stays sharp without paying for it across the whole frame. +Escher drew *Print Gallery* by hand in 1956 and left a white blot at its centre — the spiral grew too tight to finish. In 2003, **Hendrik Lenstra** and **Bart de Smit** found the exact map behind it: the idealised picture contains a copy of itself rotated **157.6256°** and shrunk by **22.5837×**. With those two numbers, they completed the picture by computer. In 2026, **3Blue1Brown** turned the whole argument into a [beautifully animated video](https://www.youtube.com/watch?v=ldxFjLJ3rVY). ---- +## Make one -## Tech +Drop in any photo, draw the rectangle where the next copy should sit, and flip between the two infinities — the straight Droste fall or the tententoon spiral. Export the loop as a PNG, GIF, or video. Everything runs in your browser: no upload, no account, no server. -| Layer | Choice | -|-------------|--------| -| UI | Svelte 5 (runes) + Vite | -| Rendering | WebGL (twgl.js), with worker-driven CPU fallback | -| State | `$state` runes, plain CSS custom properties for theming | -| Exports | `MediaRecorder` (MP4/WebM), `gifenc` (GIF), `.toBlob` (PNG) | -| Storage | `localStorage` for the last session's selection | -| Backend | none — by design | +**Live:** [silvio-tententoon.pgs.sh](https://silvio-tententoon.pgs.sh/) --- -## Layout +
+Run it locally +```sh +npm install # or: bun install +npm run dev # or: bun run dev → open the URL Vite prints +npm run build # → dist/ +npm run preview # serve dist/ locally ``` -src/ - App.svelte root: routing, bootstrap, panels - components/ - EscherPanel.svelte static Droste render - EscherZoomPanel.svelte animated spiral zoom (GPU + CPU fallback) - LogPanel.svelte log-domain view - SourcePanel.svelte the source-image picker with nested rect - UiVariant1.svelte the polished editor shell - ui1/ editor sub-components (tool rail, inspector, …) - lib/ - math/ Droste geometry, spiral, log map - render/ GL shaders, CPU worker - stores/ image + selection state - persistence.ts session restore - ui1/ editor state machine, exports -public/ - Droste_1260359-nevit.jpg default sample image (CC BY-SA 3.0, Nevit Dilmen) -``` - ---- -## Credits +Svelte 5 (runes) + Vite. Rendering is WebGL via [twgl.js](https://twgljs.org/) with a CPU-worker fallback; exports use `.toBlob` (PNG), `MediaRecorder` (MP4/WebM), and [`gifenc`](https://github.com/mattdesl/gifenc) (GIF). No backend by design. -- **The Print Gallery** — M. C. Escher, 1956. The lithograph that gave this its name and - its blind spot. -- **The mathematical completion** — Bart de Smit and Hendrik Lenstra, 2003. - *Artful Mathematics: The Heritage of M. C. Escher.* Notices of the AMS. -- **Default image** — *Droste effect* photograph by [Nevit Dilmen](https://commons.wikimedia.org/wiki/File:Droste_1260359-nevit.jpg), - used under [CC BY-SA 3.0](https://creativecommons.org/licenses/by-sa/3.0/). - ---- +
-## Licence +## Credits & licence -The code is released under the MIT licence (see `LICENSE` once added). The default sample -image carries its own CC BY-SA licence; see `public/ATTRIBUTION.txt`. +- **Print Gallery** / *Prentententoonstelling* — M. C. Escher, 1956. Escher's works are © The M. C. Escher Company; referenced here by description and link, not reproduced. +- **The mathematical completion** — Bart de Smit & Hendrik Lenstra, *The Mathematical Structure of Escher's Print Gallery*, [Notices of the AMS, 2003](https://www.ams.org/notices/200304/fea-escher.pdf). +- **Demo image** — *Droste effect* by [Nevit Dilmen](https://commons.wikimedia.org/wiki/File:Droste_1260359-nevit.jpg), [CC BY-SA 3.0](https://creativecommons.org/licenses/by-sa/3.0/) (see `public/ATTRIBUTION.txt`). +- **Code** — MIT. diff --git a/docs/screenshots/dictionary-card-desktop.png b/docs/screenshots/dictionary-card-desktop.png new file mode 100644 index 0000000000000000000000000000000000000000..781700e322cd60be48643866884f259d95c65cd9 GIT binary patch literal 202401 zcmeGBWm6nn&@Bw3gA;6UcLvws?hb>yySoQ>2sXGogS)%Cy99R#Ay^>tT=zM3pC9qo z`*HW~uC7|Ws(bg^aq6ma7^uXkFfcF}3i8sLFfedIFfg!D$Z-EzF5kOVU|_Id6r?4z z{PJ)6kwPmbwdn&Ez6klMEhuo8<)^c5>qw@-Z-pxKj#;a0g&wgIX71CCisEMmv)txJ 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zb&nVvs!9AzKK$kDQ$BimcVHP4zX(@ER5{E`5Oo zXPAILU%k9_$+u^EHCMe25ng+}h7|Dv3qCtE{6b!zEAIa%ug?eKZLiNFnU~%=o^3wf z1_b)?HZ1UW@#g;l00960^?Zxb00006Nkl + + + + +What is a tententoon? + + + + + + + + + +

+ +
+ +
+
+ + +

+ ten·ten·toon + /ˌtɛn.tɛnˈtoːn/ + noun +

+ +

+ 1. a self-repeating image whose copies spiral as + they shrink, in the manner of M. C. Escher's + Print Gallery. +

+

a tententoon of the old + gallery, winding inward without end.

+ +

+ Origin + coined from the Dutch Prentententoonstelling + (“print exhibition”): prenten, prints + + tentoonstelling, exhibition — the word lifted from where + the two halves meet. +

+
+
+ +

First, the easy version

+

+ Put a picture inside itself. Then put it inside that copy, and inside + the next, and don't stop. +

+ +
+
+ A photograph of a person holding a picture frame; inside the frame is the same person holding the same frame, repeating into the distance. +
+
+ A real photograph — a frame, inside a frame, inside a frame. The effect + is named after a tin of Droste cocoa that pulled the same trick back in 1904. +
+
+ +

+ Every copy sits squarely inside the one before it. The picture drops + straight down into itself, shrinking by the same step each time, + forever. That is the Droste effect, and you have seen it a + hundred times. +

+ +

Now bend it

+

+ Here is a stranger question. What if each copy does not only shrink — + what if it also turns? +

+ +
+
+ The same photograph, but the nested copies rotate as they shrink, winding the whole image into a smooth spiral. +
+
The same photograph, bent. Made with this tool.
+
+ +

+ Same picture. Same rule — a copy, inside a copy, inside a copy. But now + every copy is rotated a little as it shrinks, and the whole stack winds up + into a spiral. Watch the edges: straight lines bow into curves, the room + twists — and nothing tears. Follow any line inward and it meets itself + exactly. Zoom forever and you never find a seam. +

+

That second picture is a tententoon.

+ +

+ Same picture. Two infinities. One drops straight down; the other takes the + scenic route — and still arrives on time. +

+ +

Why doesn't it tear?

+

+ All of it comes from one move: take the logarithm. +

+

+ Shrinking-and-repeating is really multiplication — each copy is the last + one times some fixed ratio. And the one thing logarithms do for a living is + turn multiplication into addition. So look at the Droste picture through a + logarithm and “shrink, then repeat” becomes “slide over, then + repeat”: the endless nested frames unroll into a plain, evenly-spaced + grid. Straight. Boring. Repeating. +

+

+ Now add the turn. A copy that shrinks and rotates is, in this + logarithm-world, a slide in two directions at once — sideways and + along. So the straight grid simply tilts. Tilt a repeating + grid, then roll it back up out of the logarithm, and that tilt becomes a + spiral. A tententoon is just Escher's straight Droste, leaning over. +

+

+ And here is why it never tears. In logarithm-world the picture is only a + pattern that repeats every fixed step. Slide it by exactly one step and you + land on an identical picture — you cannot tell it moved. Roll that back + up, and “one step” becomes “one full turn of the spiral.” + The loop closes because the shift closes. The seam isn't hidden; there simply + isn't one. +

+
+ for the curious + Every point z in the picture becomes log(z − c), measured from + the centre c. One copy of the whole image is then the map
+   log(z − c) → log(z − c) + log S + iθ
+ — a shift of log S along the real axis (that's the zoom) and + θ around the imaginary one (that's the rotation). One complex number + carries both at once. That is the entire trick. +
+ +

Escher got there first — by hand

+

+ Escher had no computer in 1956. He worked the curved grid out by eye, ruled it + onto the canvas, and painted a gallery, a print, a town, and the gallery again + into the bend. And he got it right — the mathematics later showed + his intuition was very nearly exact. +

+

+ But a spiral tightens forever toward its centre, and a pen can only go so fine. + So Escher stopped, left a soft white patch in the middle of the picture, curled + his signature into it, and called it finished. The one place the picture could + not finish itself. +

+ +

The theorem that filled the hole

+

+ In 2003, two mathematicians in Leiden — Bart de Smit + and Hendrik Lenstra — wrote down the exact map hiding in + Escher's grid. The idealised Print Gallery, they showed, contains a + complete copy of itself rotated by 157.6256° and shrunk by a + factor of 22.5837. Pin those two numbers down and the entire + picture is determined — including the part Escher left blank. +

+

+ With the map in hand, they let a computer do what a pen could not: continue the + spiral inward, far past the reach of any hand, and close the white hole at last. +

+ +

See it move

+

+ If you'd like the whole argument in motion, Grant Sanderson + (of 3Blue1Brown) made a beautiful animated tour of the paper in 2026. + It is the clearest walk through the mathematics there is — + watch it here. +

+ +

Now make one

+

+ This tool does the bending for you. Drop in any photo, draw the rectangle where + the next copy should sit, and flip between the two infinities: the straight + Droste fall, or the tententoon spiral. Export the loop as a PNG, a GIF, or a + video. It all runs in your browser — no upload, no account, no server. +

+ + +
+

+ Prentententoonstelling (“Print Gallery”), + M. C. Escher, lithograph, 1956. Escher's works are + © The M. C. Escher Company — shown here by + description and link, not reproduction. +

+

+ “The Mathematical Structure of Escher's Print Gallery,” + B. de Smit & H. W. Lenstra Jr., + Notices of the AMS, 2003. + See also Wikipedia: Print Gallery. +

+

+ Demonstration photograph: “Droste effect” by + Nevit Dilmen, + CC BY-SA 3.0. +

+
+ +
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    About tententoon

    -

    A toy for re-creating the Droste effect from Escher's Print Gallery.

    +

    A toy for re-creating the Droste effect from Escher's Print Gallery.

    -
    -
    +
    @@ -443,11 +437,12 @@

    Now bend it

    what if it also turns?

    -
    -
    - The same photograph, but the nested copies rotate as they shrink, winding the whole image into a smooth spiral. +
    +
    + tententoon +
    -
    The same photograph, bent. Made with this tool.
    +
    The same photograph, wound into a spiral — rendered live, right here. That is a tententoon.

    @@ -457,7 +452,6 @@

    Now bend it

    twists — and nothing tears. Follow any line inward and it meets itself exactly. Zoom forever and you never find a seam.

    -

    That second picture is a tententoon.

    Same picture. Two infinities. One drops straight down; the other takes the @@ -469,100 +463,72 @@

    Why doesn't it tear?

    All of it comes from one move: take the logarithm.

    - Shrinking-and-repeating is really multiplication — each copy is the last - one times some fixed ratio. And the one thing logarithms do for a living is - turn multiplication into addition. So look at the Droste picture through a - logarithm and “shrink, then repeat” becomes “slide over, then - repeat”: the endless nested frames unroll into a plain, evenly-spaced - grid. Straight. Boring. Repeating. -

    -

    - Now add the turn. A copy that shrinks and rotates is, in this - logarithm-world, a slide in two directions at once — sideways and - along. So the straight grid simply tilts. Tilt a repeating - grid, then roll it back up out of the logarithm, and that tilt becomes a - spiral. A tententoon is just Escher's straight Droste, leaning over. + Measure every point by how far it sits from the centre c and at what + angle, then take the logarithm of the distance. Shrinking-and-repeating is + multiplication, and logarithms turn multiplication into addition — so the + endless nested frames unroll into a plain, repeating lattice: step + sideways by log S for one Droste jump, up or down by + for one full turn around c. Straight. Boring. Tiling forever.

    - And here is why it never tears. In logarithm-world the picture is only a - pattern that repeats every fixed step. Slide it by exactly one step and you - land on an identical picture — you cannot tell it moved. Roll that back - up, and “one step” becomes “one full turn of the spiral.” - The loop closes because the shift closes. The seam isn't hidden; there simply - isn't one. + And here is the surprise — in your fingertips. The panel on the left is + that lattice, log(z − c). Drag it. A + sideways drag zooms the original on the right; an up-and-down drag + rotates it. A slide in the log is nothing but a rotate-and-zoom back + in the original picture — that is the whole trick, and the readout keeps + the score.

    -

    The same trick, in four pictures

    -

    - Here is the whole move, live. The same photograph runs through all four frames - at once — only the ruler changes. Drag the log panel - (top-right): slide it sideways to zoom, up and down to rotate, - and watch the tententoon follow. That is the secret in your fingertips: in the - log world, sideways is scale and vertical is angle. -

    - -
    -
    -
    - source -
    the test photograph with its nest rectangle
    -
    -
    +
    +
    +
    log(z − c) drag me ↔ zoom  ↕ rotate
    -
    - rotated log - -
    -
    - tententoon - +
    + the original +
    -
    - drag the log panel — ↔ zoom, ↕ rotate - +
    +
    + drag the log panel — ↔ zoom, ↕ rotate the original + +
    + + +

    + Now add the turn for real. A copy that shrinks and rotates leans that + lattice over by a fixed angle, β = arctan(log S / 2π) + — the one tilt that lets the pattern still line up with itself after a + slide: +

    + +
    +
    + rotated log +
    - +
    The same lattice, leaned over by β. That lean is the whole difference between a Droste and an Escher.
    -
      -
    1. - The picture, and a rectangle. Mark where the next copy - belongs. That single choice fixes everything else: how far each copy shrinks - (call it S), and the one point c that all the copies rush - toward. -
    2. -
    3. - Unroll it — log(z − c). Re-measure every point by - how far it sits from c and at what angle, then take the logarithm of - the distance. The endless nested frames flatten into a plain, repeating - lattice: step sideways by log S and you have moved one - Droste jump; step up or down by and you have gone once around - c. Straight. Boring. Tiling forever. -
    4. -
    5. - Lean it over. Tilt that lattice by a fixed angle, - β = arctan(log S / 2π). Nothing tears: a pattern that - repeats every tile looks identical after you slide it by one tile, so it - survives the lean unscarred. That lean is the whole difference between a - Droste and an Escher. -
    6. -
    7. - Roll it back up. Undo the logarithm and the tilted lattice - winds into the tententoon — one seamless spiral. In a single line it is - the map w(z) = c + (z − c)α with - α = 1 − i·(log S / 2π): the real part - carries the picture, the imaginary part is the lean. -
    8. -

    - The seam never shows because in the two flat middle frames there is nothing to - tear — only a pattern, repeating. + Roll the logarithm back up and the tilted lattice winds into the spiral you saw + above — the tententoon. In a single line it is the map + w(z) = c + (z − c)α with + α = 1 − i·(log S / 2π): the real part carries + the picture, the imaginary part is the lean. +

    +

    + And here is why it never tears. In the lattice there is nothing to tear — + only a pattern that repeats. Slide it by exactly one tile and you land on an + identical picture; roll that back up and “one tile” becomes + “one full turn of the spiral.” The loop closes because the shift + closes. The seam isn't hidden; there simply isn't one.

    Escher got there first — by hand

    diff --git a/src/explain/main.ts b/src/explain/main.ts index 04a75a2..29ea718 100644 --- a/src/explain/main.ts +++ b/src/explain/main.ts @@ -1,14 +1,17 @@ /** - * Explorable for the "four pictures" section of explain.html. + * Live panels for explain.html, rendered by the app's own GPU pipeline + * renderer (PipelinePanelGLRenderer) — no duplicated math. * - * Loads a (swappable) test image, builds the Droste→Escher geometry, and - * renders the pipeline's four frames live: source · log(z−c) · rotated log · - * tententoon. It reuses the app's GPU renderer (PipelinePanelGLRenderer) and - * geometry helpers — no duplicated math. + * Three places on the page, fed by one swappable test image: + * #exp-escher — the tententoon spiral (canonical twist), in "Now bend it". + * #exp-rotlog — the rotated-log lattice, the "lean it over" illustration. + * #exp-log — log(z − c). DRAGGABLE. + #exp-orig — "the original". * - * Drag the log panel: a horizontal drag pans u = log|z−c| (a ZOOM); a vertical - * drag pans v = arg(z−c) (a ROTATION). The same pan feeds the tententoon, so - * you watch the spiral zoom and rotate under your finger. + * The experiment: dragging #exp-log pans log space. A horizontal pan is a + * shift in u = log|z − c| (a ZOOM); a vertical pan is a shift in v = arg(z − c) + * (a ROTATION). The same pan feeds #exp-orig — the picture with the spiral + * twist turned off (kTwist = 0) — so you watch a slide in the log become a + * rotate-and-zoom of the original, first-hand. */ import { fitCropToNest, type Rect } from '../lib/math/droste'; @@ -49,11 +52,12 @@ async function loadPixels(src: string): Promise { return ctx.getImageData(0, 0, c.width, c.height); } -type Panel = { canvas: HTMLCanvasElement; renderer: PipelinePanelGLRenderer; mode: PanelMode }; +type PanelDef = { id: string; mode: PanelMode; pan: boolean; kTwist?: number }; +type Panel = PanelDef & { canvas: HTMLCanvasElement; renderer: PipelinePanelGLRenderer }; async function main(): Promise { - const fig = byId('explorable'); - if (!fig) return; + const root = byId('exp-root'); + if (!root) return; const fallback = byId('exp-fallback'); const readout = byId('exp-readout'); @@ -62,10 +66,10 @@ async function main(): Promise { fallback.hidden = false; if (msg) fallback.textContent = msg; } - const grid = fig!.querySelector('.exp-grid') as HTMLElement | null; - const controls = fig!.querySelector('.exp-controls') as HTMLElement | null; - if (grid) grid.style.display = 'none'; - if (controls) controls.style.display = 'none'; + // Hide every live panel + its controls; the prose still explains it all. + document.querySelectorAll('.live-panels, .exp-controls').forEach((el) => { + el.style.display = 'none'; + }); } let pixels: ImageData; @@ -88,26 +92,14 @@ async function main(): Promise { const uRef = panelURef(ctx.rMax); const lnR0 = Math.log(Math.max(R0, 1e-9)); - // Source thumbnail + nest overlay. Every cell takes the image's aspect ratio - // (--cell-ar), so the source fills its cell with no letterbox and the nest - // box can be positioned in plain percentages. - fig.style.setProperty('--cell-ar', `${image.width} / ${image.height}`); - const srcImg = byId('exp-src'); - if (srcImg) srcImg.src = SOURCE; - const nestBox = byId('exp-nest'); - if (nestBox) { - nestBox.style.left = `${(nest.x / image.width) * 100}%`; - nestBox.style.top = `${(nest.y / image.height) * 100}%`; - nestBox.style.width = `${(nest.w / image.width) * 100}%`; - nestBox.style.height = `${(nest.h / image.height) * 100}%`; - } + // Image-aspect cells so the "original" panel shows the picture undistorted. + root.style.setProperty('--cell-ar', `${image.width} / ${image.height}`); - // GL panels — one WebGL2 context per canvas. Bail to the prose fallback if - // WebGL2 is unavailable (init throws). - const defs: Array<{ id: string; mode: PanelMode }> = [ - { id: 'exp-log', mode: 'log' }, - { id: 'exp-rotlog', mode: 'rotlog' }, - { id: 'exp-escher', mode: 'escher' } + const defs: PanelDef[] = [ + { id: 'exp-escher', mode: 'escher', pan: false }, // the spiral ("Now bend it") + { id: 'exp-rotlog', mode: 'rotlog', pan: false }, // the tilt illustration + { id: 'exp-log', mode: 'log', pan: true }, // draggable log lattice + { id: 'exp-orig', mode: 'escher', pan: true, kTwist: 0 } // "the original", no twist ]; const panels: Panel[] = []; try { @@ -116,7 +108,7 @@ async function main(): Promise { if (!canvas) continue; const renderer = new PipelinePanelGLRenderer(); renderer.init(canvas); - panels.push({ canvas, renderer, mode: d.mode }); + panels.push({ ...d, canvas, renderer }); } } catch { for (const p of panels) p.renderer.dispose(); @@ -138,15 +130,18 @@ async function main(): Promise { W = Math.max(1, Math.round(W * s)); H = Math.max(1, Math.round(H * s)); } + const panU = p.pan ? pan.u : 0; + const panV = p.pan ? pan.v : 0; if (p.mode === 'escher') { p.renderer.render({ pixels, ctx, mode: 'escher', W, H, - scale: W / ctx.W, lnR0, panU: pan.u, panV: pan.v + scale: W / ctx.W, lnR0, panU, panV, + ...(p.kTwist !== undefined ? { kTwist: p.kTwist } : {}) }); } else { p.renderer.render({ pixels, ctx, mode: p.mode, W, H, - pxPerUnit: panelPxPerUnit(p.mode, ctx.logS, H), uRef, panU: pan.u, panV: pan.v + pxPerUnit: panelPxPerUnit(p.mode, ctx.logS, H), uRef, panU, panV }); } } @@ -154,78 +149,77 @@ async function main(): Promise { function updateReadout(): void { if (!readout) return; if (pan.u === 0 && pan.v === 0) { - readout.textContent = 'drag the log panel — ↔ zoom, ↕ rotate'; + readout.textContent = 'drag the log panel — ↔ zoom, ↕ rotate the original'; return; } const zoom = Math.exp(pan.u); let deg = ((pan.v * 180) / Math.PI) % 360; if (deg < 0) deg += 360; - readout.textContent = `u-pan → zoom ×${zoom.toFixed(2)} · v-pan → rotation ${deg.toFixed(0)}°`; + readout.textContent = `the original is now zoomed ×${zoom.toFixed(2)} and rotated ${deg.toFixed(0)}°`; } let raf = 0; - function scheduleRender(): void { + let panOnly = false; + function scheduleRender(onlyPanned = false): void { + panOnly = panOnly || onlyPanned; if (raf) return; raf = requestAnimationFrame(() => { raf = 0; - for (const p of panels) renderPanel(p); + const only = panOnly; + panOnly = false; + for (const p of panels) if (!only || p.pan) renderPanel(p); updateReadout(); }); } - // Drag-to-pan: Δx → u (zoom), Δy → v (rotation). One cell-height of vertical - // drag = 2π = exactly one full turn, so the gesture maps 1:1 to the angle. - function attachPan(canvas: HTMLCanvasElement): void { + // Drag-to-pan on the log panel: Δx → u (zoom), Δy → v (rotation). One cell + // height of vertical drag = 2π = exactly one full turn. + const logCanvas = byId('exp-log'); + if (logCanvas) { let active = false; let lastX = 0; let lastY = 0; - canvas.addEventListener('pointerdown', (e) => { + logCanvas.addEventListener('pointerdown', (e) => { active = true; lastX = e.clientX; lastY = e.clientY; try { - canvas.setPointerCapture(e.pointerId); + logCanvas.setPointerCapture(e.pointerId); } catch { /* pointer not capturable (e.g. synthetic event) */ } e.preventDefault(); }); - canvas.addEventListener('pointermove', (e) => { + logCanvas.addEventListener('pointermove', (e) => { if (!active) return; - const h = canvas.getBoundingClientRect().height || 1; + const h = logCanvas.getBoundingClientRect().height || 1; const perUnit = h / TWO_PI; // css px per log-space unit pan.u += (e.clientX - lastX) / perUnit; pan.v += (e.clientY - lastY) / perUnit; lastX = e.clientX; lastY = e.clientY; - scheduleRender(); + scheduleRender(true); }); const end = (e: PointerEvent) => { active = false; try { - canvas.releasePointerCapture(e.pointerId); + logCanvas.releasePointerCapture(e.pointerId); } catch { - /* pointer already released */ + /* already released */ } }; - canvas.addEventListener('pointerup', end); - canvas.addEventListener('pointercancel', end); + logCanvas.addEventListener('pointerup', end); + logCanvas.addEventListener('pointercancel', end); } - const logCanvas = byId('exp-log'); - const rotCanvas = byId('exp-rotlog'); - if (logCanvas) attachPan(logCanvas); - if (rotCanvas) attachPan(rotCanvas); byId('exp-reset')?.addEventListener('click', () => { pan.u = 0; pan.v = 0; - scheduleRender(); + scheduleRender(true); }); - const ro = new ResizeObserver(() => scheduleRender()); - ro.observe(fig); - - scheduleRender(); + new ResizeObserver(() => scheduleRender(false)).observe(root); + scheduleRender(false); } void main(); From 3c3848166c8b3956a3a6bda9394169b7a32f1bc7 Mon Sep 17 00:00:00 2001 From: Silvio Tomatis Date: Fri, 29 May 2026 10:35:39 +0200 Subject: [PATCH 6/7] feat(explain): source modes + twist-angle control Add two controls to the explorable, both feeding the reused GPU pipeline: a source toggle (picture / grid / polar / overlay) and a twist-angle (beta) slider. src/explain/patterns.ts generates grid + polar sources centred on the limit point c at the photo's pixel size. Polar rings are individually styled (thick / dashed / plain, in ink then red) so you can follow one through the map, and spaced by S^(1/6) so the style cycle is S-periodic = seamless under the Droste fold; in the log panel each ring becomes its own vertical line. The slider overrides beta = atan(logS/2pi): the tententoon twist is tan(beta) and the rotated-log leans by beta. Only at the canonical beta does the spiral close (a 'closed' marker shows it). Verified live: circles -> vertical lines, grid warps, overlay, and a 20deg twist clearly tightens the spiral. Co-Authored-By: Claude Opus 4.8 --- docs/screenshots/explorable-polar.png | Bin 0 -> 155151 bytes explain.html | 41 ++++- src/explain/main.ts | 230 ++++++++++++++++---------- src/explain/patterns.ts | 141 ++++++++++++++++ 4 files changed, 323 insertions(+), 89 deletions(-) create mode 100644 docs/screenshots/explorable-polar.png create mode 100644 src/explain/patterns.ts diff --git a/docs/screenshots/explorable-polar.png b/docs/screenshots/explorable-polar.png new file mode 100644 index 0000000000000000000000000000000000000000..53a7a566af05a8f586a08a844318ee93d361baa2 GIT binary patch literal 155151 zcmY(KRa6{Nx2=O)aQEQu?!gJ#xVr^+m&P@CfFMBwG;YD2#x+0#!QI`RzB%XKf1G<> zYSly4SbOZ+RkhbQ=ZXcW%A=!_pnmx90sV`DjK+r#uz~;1?~!5u9l;`#86Q4iefT0H zspXq{`i5j?r0-7=v#!;KDg;N{o9pq_8)MGg-@lzt=nKh8>cX|Kol`BX;q-}dPuX3g z)oAl;Ue|q1mwy9W!Yusc?XRh}oS%QKc;u7eQK;b}$F|lV-k>NC1jxw>r$;Hih+w(G ziYc)Tv4eLZ!KK@nKJbm`)%fOoB}dQeb)j_h^UF(gRJ8k2u3Nw=Ma%Hn{|%FJqS!7j 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color: var(--accent); } .exp-fallback { font-family: Inter, system-ui, sans-serif; font-size: 13.5px; color: var(--muted); } + .angle-ctl { display: inline-flex; align-items: center; gap: 9px; } + .angle-ctl em { font-style: italic; } + .angle-ctl input[type="range"] { width: 150px; accent-color: var(--accent); cursor: pointer; } + .angle-ctl .aval { font-variant-numeric: tabular-nums; min-width: 96px; } + .angle-ctl .aval.closed { color: var(--accent-deep); font-weight: 700; } + + .seg { display: inline-flex; align-items: center; gap: 6px; flex-wrap: wrap; } + .seg .seg-label { color: var(--muted); } + .seg button { + font-family: inherit; + font-size: 12px; + font-weight: 600; + color: var(--ink-2); + background: var(--panel); + border: 1px solid var(--rule); + border-radius: 7px; + padding: 5px 11px; + cursor: pointer; + } + .seg button:hover { border-color: var(--accent); color: var(--accent); } + .seg button.on { background: var(--accent); color: #fff; border-color: var(--accent); } + .cta-row { margin: 2em 0 1em; } .cta { display: inline-block; @@ -442,8 +464,12 @@

    Now bend it

    tententoon
    -
    The same photograph, wound into a spiral — rendered live, right here. That is a tententoon.
    +
    A live tententoon — the source, wound into a spiral.
    +
    + + +

    Same picture. Same rule — a copy, inside a copy, inside a copy. But now @@ -476,9 +502,20 @@

    Why doesn't it tear?

    sideways drag zooms the original on the right; an up-and-down drag rotates it. A slide in the log is nothing but a rotate-and-zoom back in the original picture — that is the whole trick, and the readout keeps - the score. + the score. Feed the same machine something cleaner, too: a grid, or polar + circles — each ring styled so you can follow it through the bend.

    +
    + + show + + + + + +
    +
    diff --git a/src/explain/main.ts b/src/explain/main.ts index 29ea718..cd38206 100644 --- a/src/explain/main.ts +++ b/src/explain/main.ts @@ -1,59 +1,56 @@ /** * Live panels for explain.html, rendered by the app's own GPU pipeline - * renderer (PipelinePanelGLRenderer) — no duplicated math. + * renderer (PipelinePanelGLRenderer) — no duplicated map math. * - * Three places on the page, fed by one swappable test image: - * #exp-escher — the tententoon spiral (canonical twist), in "Now bend it". - * #exp-rotlog — the rotated-log lattice, the "lean it over" illustration. + * #exp-escher — the tententoon spiral, in "Now bend it". Its twist follows + * the angle slider, so you see how β shapes the final spiral. + * #exp-rotlog — the rotated-log lattice (leans by the same angle). * #exp-log — log(z − c). DRAGGABLE. + #exp-orig — "the original". * - * The experiment: dragging #exp-log pans log space. A horizontal pan is a - * shift in u = log|z − c| (a ZOOM); a vertical pan is a shift in v = arg(z − c) - * (a ROTATION). The same pan feeds #exp-orig — the picture with the spiral - * twist turned off (kTwist = 0) — so you watch a slide in the log become a - * rotate-and-zoom of the original, first-hand. + * Two global controls feed every panel from one swappable test image: + * • source mode — picture / grid / polar / overlay (see patterns.ts). + * • twist angle — overrides β = atan(logS / 2π); only at β does the spiral + * close on itself. + * + * The experiment: dragging #exp-log pans log space. Horizontal pan = a shift in + * u = log|z − c| (a ZOOM); vertical pan = a shift in v = arg(z − c) (a + * ROTATION). The same pan drives #exp-orig (the picture with the twist off), so + * a slide in the log visibly becomes a rotate-and-zoom of the original. */ import { fitCropToNest, type Rect } from '../lib/math/droste'; import { buildPanelGeometry, panelPxPerUnit, panelURef } from '../lib/ui1/pipeline-panels'; -import { PipelinePanelGLRenderer, type PanelMode } from '../lib/render/pipeline-gl'; +import { PipelinePanelGLRenderer } from '../lib/render/pipeline-gl'; +import { makeSource, type SourceMode } from './patterns'; // ─── Swappable test image ─────────────────────────────────────────────────── // To use a different picture: drop it in /public and point SOURCE at it. NEST -// is the nest rectangle in *image pixels* — load the image in the editor, draw -// the rectangle, and read x / y / w / h off the readout. Leave NEST = null to -// drop a ~half-size nest in the centre of whatever image you give (S ≈ 2). +// is the nest rectangle in *image pixels* — load it in the editor, draw the +// rectangle, read x / y / w / h off the readout. Leave NEST = null to drop a +// ~half-size nest in the centre of whatever image you give (S ≈ 2). const SOURCE = '/Droste_1260359-nevit.jpg'; const NEST: Rect | null = { x: 343.2, y: 334.7, w: 583.5, h: 454.9 }; // ───────────────────────────────────────────────────────────────────────────── const TWO_PI = 2 * Math.PI; -const MAX_PX = 720; // cap a canvas's long side (keeps the GPU framebuffer small) +const MAX_PX = 720; const byId = (id: string) => document.getElementById(id) as T | null; function centeredNest(w: number, h: number): Rect { - const nw = w * 0.5; - const nh = h * 0.5; - return { x: (w - nw) / 2, y: (h - nh) / 2, w: nw, h: nh }; + const s = 0.5; + return { x: (w * (1 - s)) / 2, y: (h * (1 - s)) / 2, w: w * s, h: h * s }; } -async function loadPixels(src: string): Promise { +function loadImage(src: string): Promise { const img = new Image(); img.decoding = 'async'; img.src = src; - await img.decode(); - const c = document.createElement('canvas'); - c.width = img.naturalWidth; - c.height = img.naturalHeight; - const ctx = c.getContext('2d', { willReadFrequently: true }); - if (!ctx) throw new Error('2d context unavailable'); - ctx.drawImage(img, 0, 0); - return ctx.getImageData(0, 0, c.width, c.height); + return img.decode().then(() => img); } -type PanelDef = { id: string; mode: PanelMode; pan: boolean; kTwist?: number }; -type Panel = PanelDef & { canvas: HTMLCanvasElement; renderer: PipelinePanelGLRenderer }; +type Role = 'tententoon' | 'log' | 'orig' | 'rotlog'; +type Panel = { role: Role; canvas: HTMLCanvasElement; renderer: PipelinePanelGLRenderer }; async function main(): Promise { const root = byId('exp-root'); @@ -66,49 +63,57 @@ async function main(): Promise { fallback.hidden = false; if (msg) fallback.textContent = msg; } - // Hide every live panel + its controls; the prose still explains it all. document.querySelectorAll('.live-panels, .exp-controls').forEach((el) => { el.style.display = 'none'; }); } - let pixels: ImageData; + let photo: HTMLImageElement; try { - pixels = await loadPixels(SOURCE); + photo = await loadImage(SOURCE); } catch { showFallback('Could not load the test image.'); return; } - const image = { width: pixels.width, height: pixels.height }; - const nest = NEST ?? centeredNest(image.width, image.height); - const crop = fitCropToNest(image, nest, null); + const W = photo.naturalWidth; + const H = photo.naturalHeight; + const nest = NEST ?? centeredNest(W, H); + const crop = fitCropToNest({ width: W, height: H }, nest, null); const geom = buildPanelGeometry(nest, crop); if (!geom) { showFallback('That nest is degenerate — pick a smaller rectangle.'); return; } - const { ctx, R0 } = geom; + const { ctx, R0, S } = geom; const uRef = panelURef(ctx.rMax); const lnR0 = Math.log(Math.max(R0, 1e-9)); + const cImgX = crop.x + ctx.cx; + const cImgY = crop.y + ctx.cy; + const beta = Math.atan2(ctx.logS, TWO_PI); // canonical twist angle // Image-aspect cells so the "original" panel shows the picture undistorted. - root.style.setProperty('--cell-ar', `${image.width} / ${image.height}`); - - const defs: PanelDef[] = [ - { id: 'exp-escher', mode: 'escher', pan: false }, // the spiral ("Now bend it") - { id: 'exp-rotlog', mode: 'rotlog', pan: false }, // the tilt illustration - { id: 'exp-log', mode: 'log', pan: true }, // draggable log lattice - { id: 'exp-orig', mode: 'escher', pan: true, kTwist: 0 } // "the original", no twist - ]; + root.style.setProperty('--cell-ar', `${W} / ${H}`); + + // ── State ────────────────────────────────────────────────────────────── + const state = { source: 'picture' as SourceMode, angle: beta, panU: 0, panV: 0 }; + let pixels = makeSource(state.source, photo, W, H, cImgX, cImgY, S); + + const roles: Role[] = ['tententoon', 'log', 'orig', 'rotlog']; + const idByRole: Record = { + tententoon: 'exp-escher', + log: 'exp-log', + orig: 'exp-orig', + rotlog: 'exp-rotlog' + }; const panels: Panel[] = []; try { - for (const d of defs) { - const canvas = byId(d.id); + for (const role of roles) { + const canvas = byId(idByRole[role]); if (!canvas) continue; const renderer = new PipelinePanelGLRenderer(); renderer.init(canvas); - panels.push({ ...d, canvas, renderer }); + panels.push({ role, canvas, renderer }); } } catch { for (const p of panels) p.renderer.dispose(); @@ -116,64 +121,115 @@ async function main(): Promise { return; } - const pan = { u: 0, v: 0 }; - function renderPanel(p: Panel): void { const dpr = window.devicePixelRatio || 1; const r = p.canvas.getBoundingClientRect(); if (r.width === 0 || r.height === 0) return; - let W = Math.round(r.width * dpr); - let H = Math.round(r.height * dpr); - const long = Math.max(W, H); + let cw = Math.round(r.width * dpr); + let ch = Math.round(r.height * dpr); + const long = Math.max(cw, ch); if (long > MAX_PX) { const s = MAX_PX / long; - W = Math.max(1, Math.round(W * s)); - H = Math.max(1, Math.round(H * s)); + cw = Math.max(1, Math.round(cw * s)); + ch = Math.max(1, Math.round(ch * s)); } - const panU = p.pan ? pan.u : 0; - const panV = p.pan ? pan.v : 0; - if (p.mode === 'escher') { - p.renderer.render({ - pixels, ctx, mode: 'escher', W, H, - scale: W / ctx.W, lnR0, panU, panV, - ...(p.kTwist !== undefined ? { kTwist: p.kTwist } : {}) - }); - } else { - p.renderer.render({ - pixels, ctx, mode: p.mode, W, H, - pxPerUnit: panelPxPerUnit(p.mode, ctx.logS, H), uRef, panU, panV - }); + const a = state.angle; + switch (p.role) { + case 'tententoon': + p.renderer.render({ + pixels, ctx, mode: 'escher', W: cw, H: ch, + scale: cw / ctx.W, lnR0, kTwist: Math.tan(a) + }); + break; + case 'orig': // the picture itself (twist off), rotated/zoomed by the pan + p.renderer.render({ + pixels, ctx, mode: 'escher', W: cw, H: ch, + scale: cw / ctx.W, lnR0, kTwist: 0, panU: state.panU, panV: state.panV + }); + break; + case 'log': + p.renderer.render({ + pixels, ctx, mode: 'log', W: cw, H: ch, + pxPerUnit: panelPxPerUnit('log', ctx.logS, ch), uRef, panU: state.panU, panV: state.panV + }); + break; + case 'rotlog': + p.renderer.render({ + pixels, ctx, mode: 'rotlog', W: cw, H: ch, + pxPerUnit: panelPxPerUnit('rotlog', ctx.logS, ch), uRef, rot: a + }); + break; } } function updateReadout(): void { if (!readout) return; - if (pan.u === 0 && pan.v === 0) { + if (state.panU === 0 && state.panV === 0) { readout.textContent = 'drag the log panel — ↔ zoom, ↕ rotate the original'; return; } - const zoom = Math.exp(pan.u); - let deg = ((pan.v * 180) / Math.PI) % 360; + const zoom = Math.exp(state.panU); + let deg = ((state.panV * 180) / Math.PI) % 360; if (deg < 0) deg += 360; readout.textContent = `the original is now zoomed ×${zoom.toFixed(2)} and rotated ${deg.toFixed(0)}°`; } let raf = 0; - let panOnly = false; - function scheduleRender(onlyPanned = false): void { - panOnly = panOnly || onlyPanned; + let dirtyAll = false; + const dirty = new Set(); + function scheduleRender(only?: Role[]): void { + if (only) only.forEach((r) => dirty.add(r)); + else dirtyAll = true; if (raf) return; raf = requestAnimationFrame(() => { raf = 0; - const only = panOnly; - panOnly = false; - for (const p of panels) if (!only || p.pan) renderPanel(p); + const all = dirtyAll; + dirtyAll = false; + const set = new Set(dirty); + dirty.clear(); + for (const p of panels) if (all || set.has(p.role)) renderPanel(p); updateReadout(); }); } - // Drag-to-pan on the log panel: Δx → u (zoom), Δy → v (rotation). One cell - // height of vertical drag = 2π = exactly one full turn. + // ── Source mode ────────────────────────────────────────────────────────── + function setSource(mode: SourceMode): void { + state.source = mode; + pixels = makeSource(mode, photo, W, H, cImgX, cImgY, S); + document.querySelectorAll('[data-source]').forEach((b) => { + b.classList.toggle('on', b.dataset.source === mode); + }); + scheduleRender(); // new texture → re-render every panel + } + document.querySelectorAll('[data-source]').forEach((b) => { + b.addEventListener('click', () => setSource((b.dataset.source as SourceMode) ?? 'picture')); + }); + + // ── Twist angle ──────────────────────────────────────────────────────── + const angleInput = byId('exp-angle'); + const angleVal = byId('exp-angle-val'); + const betaDeg = (beta * 180) / Math.PI; + function setAngleDeg(deg: number): void { + state.angle = (deg * Math.PI) / 180; + if (angleVal) { + const closed = Math.abs(deg - betaDeg) < 0.4; + angleVal.textContent = `${deg.toFixed(1)}°${closed ? ' — closed ✓' : ''}`; + angleVal.classList.toggle('closed', closed); + } + scheduleRender(['tententoon', 'rotlog']); + } + if (angleInput) { + angleInput.min = '0'; + angleInput.max = Math.max(24, Math.ceil(betaDeg * 3)).toString(); + angleInput.step = '0.1'; + angleInput.value = betaDeg.toFixed(1); + angleInput.addEventListener('input', () => setAngleDeg(parseFloat(angleInput.value))); + setAngleDeg(betaDeg); + } + const betaNote = byId('exp-angle-note'); + if (betaNote) betaNote.textContent = `closes seamlessly at β ≈ ${betaDeg.toFixed(1)}°`; + + // ── Drag-to-pan on the log panel ───────────────────────────────────────── const logCanvas = byId('exp-log'); if (logCanvas) { let active = false; @@ -186,19 +242,19 @@ async function main(): Promise { try { logCanvas.setPointerCapture(e.pointerId); } catch { - /* pointer not capturable (e.g. synthetic event) */ + /* not capturable (synthetic event) */ } e.preventDefault(); }); logCanvas.addEventListener('pointermove', (e) => { if (!active) return; const h = logCanvas.getBoundingClientRect().height || 1; - const perUnit = h / TWO_PI; // css px per log-space unit - pan.u += (e.clientX - lastX) / perUnit; - pan.v += (e.clientY - lastY) / perUnit; + const perUnit = h / TWO_PI; // one cell height = 2π = one full turn + state.panU += (e.clientX - lastX) / perUnit; + state.panV += (e.clientY - lastY) / perUnit; lastX = e.clientX; lastY = e.clientY; - scheduleRender(true); + scheduleRender(['log', 'orig']); }); const end = (e: PointerEvent) => { active = false; @@ -213,13 +269,13 @@ async function main(): Promise { } byId('exp-reset')?.addEventListener('click', () => { - pan.u = 0; - pan.v = 0; - scheduleRender(true); + state.panU = 0; + state.panV = 0; + scheduleRender(['log', 'orig']); }); - new ResizeObserver(() => scheduleRender(false)).observe(root); - scheduleRender(false); + new ResizeObserver(() => scheduleRender()).observe(root); + scheduleRender(); } void main(); diff --git a/src/explain/patterns.ts b/src/explain/patterns.ts new file mode 100644 index 0000000..21181a8 --- /dev/null +++ b/src/explain/patterns.ts @@ -0,0 +1,141 @@ +/** + * Source content for the explain.html explorable. + * + * Four modes feed the same pipeline so you can watch the Droste→Escher map act + * on different things: + * picture — the test photograph. + * grid — a cartesian grid centred on the limit point c. + * polar — concentric circles + spokes centred on c. Each circle has its + * own style (thick / dashed / plain, in ink then red) so you can + * follow an individual ring through the transform; in the log + * panel a circle becomes a vertical line. + * overlay — the photograph with the grid and polar drawn on top. + * + * Patterns are drawn at the photo's pixel size, centred on c (image coords), + * and the rings are spaced by S^(1/6) so the style cycle repeats exactly once + * per Droste period — i.e. the pattern is invariant under scaling by S about + * c, the same self-similarity the photo has, so the fold stays seamless. + */ + +export type SourceMode = 'picture' | 'grid' | 'polar' | 'overlay'; + +const INK = '#26424a'; +const RED = '#d1495b'; +const RINGS_PER_PERIOD = 6; + +type RingStyle = { width: number; dash: number[]; color: string }; + +function ringStyle(n: number, overlay: boolean): RingStyle { + const ink = overlay ? 'rgba(255,255,255,0.92)' : INK; + const red = overlay ? '#ff6b7a' : RED; + const cycle: RingStyle[] = [ + { width: 5, dash: [], color: ink }, // thick + { width: 2.5, dash: [11, 9], color: ink }, // dashed + { width: 2.5, dash: [], color: ink }, // plain + { width: 5, dash: [], color: red }, // thick red + { width: 2.5, dash: [11, 9], color: red }, // dashed red + { width: 2.5, dash: [], color: red } // plain red + ]; + return cycle[((n % RINGS_PER_PERIOD) + RINGS_PER_PERIOD) % RINGS_PER_PERIOD]; +} + +function line(ctx: CanvasRenderingContext2D, x1: number, y1: number, x2: number, y2: number): void { + ctx.beginPath(); + ctx.moveTo(x1, y1); + ctx.lineTo(x2, y2); + ctx.stroke(); +} + +function drawGrid(ctx: CanvasRenderingContext2D, W: number, H: number, cx: number, cy: number, overlay: boolean): void { + const step = Math.min(W, H) / 16; + ctx.save(); + ctx.lineWidth = 1.5; + ctx.strokeStyle = overlay ? 'rgba(255,255,255,0.42)' : 'rgba(43,58,66,0.30)'; + for (let x = cx % step; x < W; x += step) line(ctx, Math.round(x) + 0.5, 0, Math.round(x) + 0.5, H); + for (let y = cy % step; y < H; y += step) line(ctx, 0, Math.round(y) + 0.5, W, Math.round(y) + 0.5); + // Coloured axes through c, so orientation is trackable through the warp. + ctx.lineWidth = overlay ? 3 : 4; + ctx.strokeStyle = overlay ? '#ff6b7a' : RED; + line(ctx, 0, cy, W, cy); + ctx.strokeStyle = overlay ? '#74c0ff' : '#2e86ab'; + line(ctx, cx, 0, cx, H); + ctx.restore(); +} + +function drawPolar(ctx: CanvasRenderingContext2D, W: number, H: number, cx: number, cy: number, S: number, overlay: boolean): void { + // Reach past the farthest corner so the rings fill the frame. + const maxR = Math.hypot(Math.max(cx, W - cx), Math.max(cy, H - cy)) + 4; + const ratio = Math.pow(Math.max(S, 1.001), 1 / RINGS_PER_PERIOD); + + ctx.save(); + // Spokes first (under the rings) — a spoke is a horizontal line in the log. + ctx.lineWidth = 1.5; + ctx.strokeStyle = overlay ? 'rgba(255,255,255,0.45)' : 'rgba(43,58,66,0.28)'; + for (let s = 0; s < 12; s++) { + const a = (s * Math.PI) / 6; + line(ctx, cx, cy, cx + Math.cos(a) * maxR, cy + Math.sin(a) * maxR); + } + // One red reference spoke at θ = 0. + ctx.lineWidth = 3; + ctx.strokeStyle = overlay ? '#ff6b7a' : RED; + line(ctx, cx, cy, cx + maxR, cy); + + // Rings, outermost in. Styles cycle every period (×S) → S-invariant, seamless. + let r = maxR; + let n = 0; + while (r > 3) { + const st = ringStyle(n, overlay); + ctx.lineWidth = st.width; + ctx.setLineDash(st.dash); + ctx.strokeStyle = st.color; + ctx.beginPath(); + ctx.arc(cx, cy, r, 0, Math.PI * 2); + ctx.stroke(); + r /= ratio; + n++; + } + ctx.setLineDash([]); + ctx.fillStyle = overlay ? '#fff' : INK; + ctx.beginPath(); + ctx.arc(cx, cy, 4, 0, Math.PI * 2); + ctx.fill(); + ctx.restore(); +} + +/** + * Render the chosen source to an ImageData at the photo's pixel size. `c` is + * the limit point in image coordinates; `S` the Droste scale (for ring + * spacing). The pipeline samples this exactly like a loaded photo. + */ +export function makeSource( + mode: SourceMode, + photo: CanvasImageSource, + W: number, + H: number, + cx: number, + cy: number, + S: number +): ImageData { + const canvas = document.createElement('canvas'); + canvas.width = W; + canvas.height = H; + const ctx = canvas.getContext('2d', { willReadFrequently: true }); + if (!ctx) throw new Error('2d context unavailable'); + + if (mode === 'picture' || mode === 'overlay') { + ctx.drawImage(photo, 0, 0, W, H); + if (mode === 'overlay') { + ctx.fillStyle = 'rgba(18,14,8,0.30)'; // mute the photo so the lines read + ctx.fillRect(0, 0, W, H); + } + } else { + ctx.fillStyle = '#f3efe6'; + ctx.fillRect(0, 0, W, H); + } + + const overlay = mode === 'overlay'; + if (mode === 'grid' || overlay) drawGrid(ctx, W, H, cx, cy, overlay); + if (mode === 'polar' || overlay) drawPolar(ctx, W, H, cx, cy, S, overlay); + + return ctx.getImageData(0, 0, W, H); +} From 2e1199de11b71b9f4bdbfd69e4bdcd3765e27c69 Mon Sep 17 00:00:00 2001 From: Silvio Tomatis Date: Fri, 29 May 2026 12:35:06 +0200 Subject: [PATCH 7/7] docs(explain): fix the de Smit-Lenstra framing, and a voice pass It was never a theorem. de Smit and Lenstra worked out the exact map (the structure) hiding in Escher's grid, and the missing centre was then filled by computer. That is analysis plus a method/recipe, not a theorem. Rename the heading 'The theorem that filled the hole' -> 'The map that filled the hole', say 'worked out' (not 'wrote down'), and call the distinction out in the text ('this is not a theorem so much as a recipe'). Voice pass over the prose per the writing profile: drop em-dash connectors throughout (colons / parentheses / periods instead) and remove 'seamlessly' from the UI copy. Code comments left untouched (not published prose). Co-Authored-By: Claude Opus 4.8 --- explain.html | 81 +++++++++++++++++++++++---------------------- src/explain/main.ts | 8 ++--- 2 files changed, 45 insertions(+), 44 deletions(-) diff --git a/explain.html b/explain.html index 58f3c63..e2c1ce1 100644 --- a/explain.html +++ b/explain.html @@ -4,7 +4,7 @@ What is a tententoon? - + @@ -424,7 +424,7 @@ Origin coined from the Dutch Prentententoonstelling (“print exhibition”): prenten, prints + - tentoonstelling, exhibition — the word lifted from where + tentoonstelling, exhibition. The coined word sits right where the two halves meet.

    @@ -441,7 +441,7 @@

    First, the easy version

    A photograph of a person holding a picture frame; inside the frame is the same person holding the same frame, repeating into the distance.
    - A real photograph — a frame, inside a frame, inside a frame. The effect + A real photograph: a frame, inside a frame, inside a frame. The effect is named after a tin of Droste cocoa that pulled the same trick back in 1904.
    @@ -455,8 +455,8 @@

    First, the easy version

    Now bend it

    - Here is a stranger question. What if each copy does not only shrink — - what if it also turns? + Here is a stranger question. What if each copy does not only shrink? What + if it also turns?

    @@ -464,7 +464,7 @@

    Now bend it

    tententoon
    -
    A live tententoon — the source, wound into a spiral.
    +
    A live tententoon: the source, wound into a spiral.
    @@ -472,16 +472,16 @@

    Now bend it

    - Same picture. Same rule — a copy, inside a copy, inside a copy. But now - every copy is rotated a little as it shrinks, and the whole stack winds up - into a spiral. Watch the edges: straight lines bow into curves, the room - twists — and nothing tears. Follow any line inward and it meets itself - exactly. Zoom forever and you never find a seam. + Same picture. Same rule: a copy, inside a copy, inside a copy. But now every + copy is rotated a little as it shrinks, and the whole stack winds up into a + spiral. Watch the edges: straight lines bow into curves, the room twists, and + nothing tears. Follow any line inward and it meets itself exactly. Zoom + forever and you never find a seam.

    Same picture. Two infinities. One drops straight down; the other takes the - scenic route — and still arrives on time. + scenic route, and still arrives on time.

    Why doesn't it tear?

    @@ -491,19 +491,19 @@

    Why doesn't it tear?

    Measure every point by how far it sits from the centre c and at what angle, then take the logarithm of the distance. Shrinking-and-repeating is - multiplication, and logarithms turn multiplication into addition — so the + multiplication, and logarithms turn multiplication into addition, so the endless nested frames unroll into a plain, repeating lattice: step sideways by log S for one Droste jump, up or down by for one full turn around c. Straight. Boring. Tiling forever.

    - And here is the surprise — in your fingertips. The panel on the left is - that lattice, log(z − c). Drag it. A + And here is the surprise, in your fingertips. The panel on the left is that + lattice, log(z − c). Drag it. A sideways drag zooms the original on the right; an up-and-down drag rotates it. A slide in the log is nothing but a rotate-and-zoom back - in the original picture — that is the whole trick, and the readout keeps - the score. Feed the same machine something cleaner, too: a grid, or polar - circles — each ring styled so you can follow it through the bend. + in the original picture. That is the whole trick, and the readout keeps the + score. Feed the same machine something cleaner, too: a grid, or polar circles + with each ring styled so you can follow it through the bend.

    @@ -530,7 +530,7 @@

    Why doesn't it tear?

    - drag the log panel — ↔ zoom, ↕ rotate the original + drag the log panel: ↔ zoom, ↕ rotate the original

    Why doesn't it tear?

    Now add the turn for real. A copy that shrinks and rotates leans that - lattice over by a fixed angle, β = arctan(log S / 2π) - — the one tilt that lets the pattern still line up with itself after a - slide: + lattice over by a fixed angle, β = arctan(log S / 2π). It + is the one tilt that lets the pattern line up with itself again after a slide:

    @@ -555,25 +554,25 @@

    Why doesn't it tear?

    Roll the logarithm back up and the tilted lattice winds into the spiral you saw - above — the tententoon. In a single line it is the map + above: the tententoon. In a single line it is the map w(z) = c + (z − c)α with α = 1 − i·(log S / 2π): the real part carries the picture, the imaginary part is the lean.

    - And here is why it never tears. In the lattice there is nothing to tear — + And here is why it never tears. In the lattice there is nothing to tear, only a pattern that repeats. Slide it by exactly one tile and you land on an identical picture; roll that back up and “one tile” becomes “one full turn of the spiral.” The loop closes because the shift closes. The seam isn't hidden; there simply isn't one.

    -

    Escher got there first — by hand

    +

    Escher got there first, by hand

    Escher had no computer in 1956. He worked the curved grid out by eye, ruled it onto the canvas, and painted a gallery, a print, a town, and the gallery again - into the bend. And he got it right — the mathematics later showed - his intuition was very nearly exact. + into the bend. And he got it right: the mathematics later showed his + intuition was very nearly exact.

    But a spiral tightens forever toward its centre, and a pen can only go so fine. @@ -582,25 +581,27 @@

    Escher got there first — by hand

    not finish itself.

    -

    The theorem that filled the hole

    +

    The map that filled the hole

    - In 2003, two mathematicians in Leiden — Bart de Smit - and Hendrik Lenstra — wrote down the exact map hiding in - Escher's grid. The idealised Print Gallery, they showed, contains a - complete copy of itself rotated by 157.6256° and shrunk by a - factor of 22.5837. Pin those two numbers down and the entire - picture is determined — including the part Escher left blank. + In 2003, two mathematicians in Leiden (Bart de Smit and + Hendrik Lenstra) worked out the exact map hiding in Escher's + grid. The idealised Print Gallery, they showed, contains a complete + copy of itself rotated by 157.6256° and shrunk by a factor + of 22.5837. Pin those two numbers down and the rest of the + picture is forced, including the part Escher left blank.

    - With the map in hand, they let a computer do what a pen could not: continue the - spiral inward, far past the reach of any hand, and close the white hole at last. + This is not a theorem so much as a recipe: with the map in hand, you can hand + the missing centre to a computer and have it do what a pen could not. That is + exactly what they did, continuing the spiral inward far past the reach of any + hand and closing the white hole at last.

    See it move

    If you'd like the whole argument in motion, Grant Sanderson (of 3Blue1Brown) made a beautiful animated tour of the paper in 2026. - It is the clearest walk through the mathematics there is — + It is the clearest walk through the mathematics there is: watch it here.

    @@ -609,7 +610,7 @@

    Now make one

    This tool does the bending for you. Drop in any photo, draw the rectangle where the next copy should sit, and flip between the two infinities: the straight Droste fall, or the tententoon spiral. Export the loop as a PNG, a GIF, or a - video. It all runs in your browser — no upload, no account, no server. + video. It all runs in your browser: no upload, no account, no server.

    Open the tool → @@ -619,8 +620,8 @@

    Now make one

    Prentententoonstelling (“Print Gallery”), M. C. Escher, lithograph, 1956. Escher's works are - © The M. C. Escher Company — shown here by - description and link, not reproduction. + © The M. C. Escher Company (shown here by + description and link, not reproduction).

    “The Mathematical Structure of Escher's Print Gallery,” diff --git a/src/explain/main.ts b/src/explain/main.ts index cd38206..a1a9d8c 100644 --- a/src/explain/main.ts +++ b/src/explain/main.ts @@ -82,7 +82,7 @@ async function main(): Promise { const crop = fitCropToNest({ width: W, height: H }, nest, null); const geom = buildPanelGeometry(nest, crop); if (!geom) { - showFallback('That nest is degenerate — pick a smaller rectangle.'); + showFallback('That nest is degenerate. Pick a smaller rectangle.'); return; } const { ctx, R0, S } = geom; @@ -165,7 +165,7 @@ async function main(): Promise { function updateReadout(): void { if (!readout) return; if (state.panU === 0 && state.panV === 0) { - readout.textContent = 'drag the log panel — ↔ zoom, ↕ rotate the original'; + readout.textContent = 'drag the log panel: ↔ zoom, ↕ rotate the original'; return; } const zoom = Math.exp(state.panU); @@ -213,7 +213,7 @@ async function main(): Promise { state.angle = (deg * Math.PI) / 180; if (angleVal) { const closed = Math.abs(deg - betaDeg) < 0.4; - angleVal.textContent = `${deg.toFixed(1)}°${closed ? ' — closed ✓' : ''}`; + angleVal.textContent = `${deg.toFixed(1)}°${closed ? ' · closed ✓' : ''}`; angleVal.classList.toggle('closed', closed); } scheduleRender(['tententoon', 'rotlog']); @@ -227,7 +227,7 @@ async function main(): Promise { setAngleDeg(betaDeg); } const betaNote = byId('exp-angle-note'); - if (betaNote) betaNote.textContent = `closes seamlessly at β ≈ ${betaDeg.toFixed(1)}°`; + if (betaNote) betaNote.textContent = `closes on itself at β ≈ ${betaDeg.toFixed(1)}°`; // ── Drag-to-pan on the log panel ───────────────────────────────────────── const logCanvas = byId('exp-log');

    + +

    Inspired by M. C. Escher's lithograph Prentententoonstelling (1956) — Dutch for From 970d7983758cfdbb15d7d7e6f5adcae024f92acb Mon Sep 17 00:00:00 2001 From: Silvio Tomatis Date: Fri, 29 May 2026 00:16:16 +0200 Subject: [PATCH 2/7] docs(explain): add four-step pipeline walkthrough Fold in the math from the feat/pipeline-explorable-view worktree's 4-panel view: source + rect -> log(z-c) lattice (periods logS, 2pi) -> tilt by beta = arctan(logS/2pi) -> roll back up via w(z) = c + (z-c)^alpha. Turns the 'why doesn't it tear' section from intuition into the concrete four frames the maths passes through, with named parameters. Drops the earlier complex-map aside, now redundant (step 4 carries the exact map). Co-Authored-By: Claude Opus 4.8 --- public/explain.html | 51 +++++++++++++++++++++++++++++++++++++-------- 1 file changed, 42 insertions(+), 9 deletions(-) diff --git a/public/explain.html b/public/explain.html index 14b73ff..2c4959e 100644 --- a/public/explain.html +++ b/public/explain.html @@ -240,6 +240,11 @@ margin-bottom: 7px; } .aside b { color: var(--accent-deep); } + .steps { margin: 1.5em 0; padding-left: 1.35em; } + .steps li { margin: 0.9em 0; line-height: 1.55; padding-left: 0.25em; } + .steps li::marker { color: var(--accent); font-weight: 700; } + .steps em { font-style: italic; } + .steps sup { font-size: 0.72em; } .cta-row { margin: 2em 0 1em; } .cta { @@ -422,15 +427,43 @@

    Why doesn't it tear?

    The loop closes because the shift closes. The seam isn't hidden; there simply isn't one.

    -
    - for the curious - Every point z in the picture becomes log(z − c), measured from - the centre c. One copy of the whole image is then the map
    -   log(z − c) → log(z − c) + log S + iθ
    - — a shift of log S along the real axis (that's the zoom) and - θ around the imaginary one (that's the rotation). One complex number - carries both at once. That is the entire trick. -
    +

    The same trick, in four pictures

    +

    Here is the whole move, broken into the four frames the mathematics actually passes through.

    +
      +
    1. + The picture, and a rectangle. Mark where the next copy + belongs. That single choice fixes everything else: how far each copy shrinks + (call it S), and the one point c that all the copies rush + toward. +
    2. +
    3. + Unroll it — log(z − c). Re-measure every point by + how far it sits from c and at what angle, then take the logarithm of + the distance. The endless nested frames flatten into a plain, repeating + lattice: step sideways by log S and you have moved one + Droste jump; step up or down by and you have gone once around + c. Straight. Boring. Tiling forever. +
    4. +
    5. + Lean it over. Tilt that lattice by a fixed angle, + β = arctan(log S / 2π). Nothing tears: a pattern that + repeats every tile looks identical after you slide it by one tile, so it + survives the lean unscarred. That lean is the whole difference between a + Droste and an Escher. +
    6. +
    7. + Roll it back up. Undo the logarithm and the tilted lattice + winds into the tententoon — one seamless spiral. In a single line it is + the map w(z) = c + (z − c)α with + α = 1 − i·(log S / 2π): the real part + carries the picture, the imaginary part is the lean. +
    8. +
    +

    + The same photograph sits in all four frames; only the ruler changes. The seam + never shows because in the two flat middle frames there is nothing to tear + — only a pattern, repeating. +

    Escher got there first — by hand

    From b784a25da35bfc031d97128664a5b0742ecc8fb1 Mon Sep 17 00:00:00 2001 From: Silvio Tomatis Date: Fri, 29 May 2026 09:14:51 +0200 Subject: [PATCH 3/7] feat(explain): turn the explainer into a live explorable explain.html moves from public/ (static) to a Vite entry (added to rollupOptions.input) with src/explain/main.ts. It loads a swappable test image (SOURCE + optional NEST consts at the top of main.ts), builds the Droste geometry with fitCropToNest/buildPanelGeometry, and renders source - log(z-c) - rotated-log - tententoon live via the app's PipelinePanelGLRenderer. No duplicated math: the page reuses the same GPU renderer and geometry helpers the in-app pipeline view uses. Dragging the log panel pans log space: horizontal pan = zoom, vertical pan = rotation, and the tententoon follows with a live readout (verified at 144 deg / x33). Falls back to the four-step prose if WebGL2 is unavailable. Removes the now-superseded static public/explain.html. Co-Authored-By: Claude Opus 4.8 --- public/explain.html => explain.html | 173 ++++++++++++++++----- src/explain/main.ts | 231 ++++++++++++++++++++++++++++ vite.config.ts | 11 ++ 3 files changed, 379 insertions(+), 36 deletions(-) rename public/explain.html => explain.html (81%) create mode 100644 src/explain/main.ts diff --git a/public/explain.html b/explain.html similarity index 81% rename from public/explain.html rename to explain.html index 2c4959e..252b194 100644 --- a/public/explain.html +++ b/explain.html @@ -4,7 +4,7 @@ What is a tententoon? - + @@ -70,15 +70,6 @@ .wrap { max-width: var(--maxw); margin: 0 auto; padding: 0 22px; } header.hero { padding: 64px 0 8px; } - .eyebrow { - font-family: Inter, system-ui, sans-serif; - text-transform: uppercase; - letter-spacing: 0.18em; - font-size: 12px; - font-weight: 600; - color: var(--muted); - margin: 0 0 14px; - } h1 { font-size: 68px; line-height: 1; @@ -218,34 +209,106 @@ } .pull b { color: var(--accent-deep); font-style: italic; } - .aside { - font-family: ui-monospace, "SF Mono", Menlo, Consolas, monospace; - font-size: 13.5px; - line-height: 1.7; - background: var(--panel); - border: 1px solid var(--rule); - border-radius: 9px; - padding: 15px 17px; - color: var(--ink-2); - margin: 1.7em 0; - } - .aside .lbl { - display: block; - font-family: Inter, system-ui, sans-serif; - text-transform: uppercase; - letter-spacing: 0.14em; - font-size: 10.5px; - font-weight: 700; - color: var(--muted); - margin-bottom: 7px; - } - .aside b { color: var(--accent-deep); } .steps { margin: 1.5em 0; padding-left: 1.35em; } .steps li { margin: 0.9em 0; line-height: 1.55; padding-left: 0.25em; } .steps li::marker { color: var(--accent); font-weight: 700; } .steps em { font-style: italic; } .steps sup { font-size: 0.72em; } + /* ── Live explorable (src/explain/main.ts) ───────────────────────────── */ + .explorable { margin: 1.6em 0 0.4em; } + .exp-grid { + display: grid; + grid-template-columns: 1fr 1fr; + gap: 8px; + background: var(--frame); + padding: 8px; + border-radius: 11px; + box-shadow: 0 14px 38px rgba(20, 14, 10, 0.18); + } + .exp-grid .cell { + position: relative; + aspect-ratio: var(--cell-ar, 4 / 3); + background: #000; + border-radius: 5px; + overflow: hidden; + } + .exp-grid canvas { display: block; width: 100%; height: 100%; } + .exp-grid .src-wrap { position: absolute; inset: 0; } + .exp-grid .src-wrap img { width: 100%; height: 100%; object-fit: fill; display: block; } + .exp-grid .nest { + position: absolute; + border: 2px solid var(--accent); + box-shadow: 0 0 0 4000px rgba(0, 0, 0, 0.22); + pointer-events: none; + } + #exp-log, #exp-rotlog { cursor: grab; touch-action: none; } + #exp-log:active, #exp-rotlog:active { cursor: grabbing; } + .plabel { + position: absolute; + left: 7px; + top: 7px; + z-index: 2; + font-family: Inter, system-ui, sans-serif; + font-size: 11px; + font-weight: 600; + color: #fff; + background: rgba(0, 0, 0, 0.5); + padding: 2px 7px; + border-radius: 4px; + display: inline-flex; + gap: 6px; + align-items: center; + pointer-events: none; + } + .plabel .pchip { + font-weight: 700; + font-size: 9.5px; + letter-spacing: 0.03em; + text-transform: uppercase; + color: #1b140e; + background: var(--accent); + padding: 1px 5px; + border-radius: 3px; + } + .draghint { + position: absolute; + right: 7px; + bottom: 7px; + z-index: 2; + font-family: Inter, system-ui, sans-serif; + font-size: 10px; + color: rgba(255, 255, 255, 0.78); + background: rgba(0, 0, 0, 0.4); + padding: 2px 7px; + border-radius: 4px; + pointer-events: none; + } + .exp-controls { + display: flex; + align-items: center; + justify-content: space-between; + gap: 12px; + margin-top: 9px; + font-family: Inter, system-ui, sans-serif; + font-size: 13px; + color: var(--ink-2); + } + .exp-controls .readout { font-variant-numeric: tabular-nums; } + .exp-controls button { + font-family: inherit; + font-size: 12px; + font-weight: 600; + color: var(--accent-deep); + background: var(--panel); + border: 1px solid var(--rule); + border-radius: 7px; + padding: 5px 13px; + cursor: pointer; + } + .exp-controls button:hover { border-color: var(--accent); color: var(--accent); } + .exp-fallback { font-family: Inter, system-ui, sans-serif; font-size: 13.5px; color: var(--muted); } + .cta-row { margin: 2em 0 1em; } .cta { display: inline-block; @@ -286,6 +349,7 @@ .sense { font-size: 17.5px; } .eg { font-size: 15px; } .pull { font-size: 22px; padding-left: 18px; } + .exp-controls { flex-direction: column; align-items: flex-start; gap: 7px; } } @@ -427,8 +491,45 @@

    Why doesn't it tear?

    The loop closes because the shift closes. The seam isn't hidden; there simply isn't one.

    +

    The same trick, in four pictures

    -

    Here is the whole move, broken into the four frames the mathematics actually passes through.

    +

    + Here is the whole move, live. The same photograph runs through all four frames + at once — only the ruler changes. Drag the log panel + (top-right): slide it sideways to zoom, up and down to rotate, + and watch the tententoon follow. That is the secret in your fingertips: in the + log world, sideways is scale and vertical is angle. +

    + +
    +
    +
    + source +
    the test photograph with its nest rectangle
    +
    +
    + log(z − c) drag me + + ↔ zoom  ↕ rotate +
    +
    + rotated log + +
    +
    + tententoon + +
    +
    +
    + drag the log panel — ↔ zoom, ↕ rotate + +
    + +
    +
    1. The picture, and a rectangle. Mark where the next copy @@ -460,9 +561,8 @@

      The same trick, in four pictures

    - The same photograph sits in all four frames; only the ruler changes. The seam - never shows because in the two flat middle frames there is nothing to tear - — only a pattern, repeating. + The seam never shows because in the two flat middle frames there is nothing to + tear — only a pattern, repeating.

    Escher got there first — by hand

    @@ -533,5 +633,6 @@

    Now make one

    + diff --git a/src/explain/main.ts b/src/explain/main.ts new file mode 100644 index 0000000..04a75a2 --- /dev/null +++ b/src/explain/main.ts @@ -0,0 +1,231 @@ +/** + * Explorable for the "four pictures" section of explain.html. + * + * Loads a (swappable) test image, builds the Droste→Escher geometry, and + * renders the pipeline's four frames live: source · log(z−c) · rotated log · + * tententoon. It reuses the app's GPU renderer (PipelinePanelGLRenderer) and + * geometry helpers — no duplicated math. + * + * Drag the log panel: a horizontal drag pans u = log|z−c| (a ZOOM); a vertical + * drag pans v = arg(z−c) (a ROTATION). The same pan feeds the tententoon, so + * you watch the spiral zoom and rotate under your finger. + */ + +import { fitCropToNest, type Rect } from '../lib/math/droste'; +import { buildPanelGeometry, panelPxPerUnit, panelURef } from '../lib/ui1/pipeline-panels'; +import { PipelinePanelGLRenderer, type PanelMode } from '../lib/render/pipeline-gl'; + +// ─── Swappable test image ─────────────────────────────────────────────────── +// To use a different picture: drop it in /public and point SOURCE at it. NEST +// is the nest rectangle in *image pixels* — load the image in the editor, draw +// the rectangle, and read x / y / w / h off the readout. Leave NEST = null to +// drop a ~half-size nest in the centre of whatever image you give (S ≈ 2). +const SOURCE = '/Droste_1260359-nevit.jpg'; +const NEST: Rect | null = { x: 343.2, y: 334.7, w: 583.5, h: 454.9 }; +// ───────────────────────────────────────────────────────────────────────────── + +const TWO_PI = 2 * Math.PI; +const MAX_PX = 720; // cap a canvas's long side (keeps the GPU framebuffer small) + +const byId = (id: string) => document.getElementById(id) as T | null; + +function centeredNest(w: number, h: number): Rect { + const nw = w * 0.5; + const nh = h * 0.5; + return { x: (w - nw) / 2, y: (h - nh) / 2, w: nw, h: nh }; +} + +async function loadPixels(src: string): Promise { + const img = new Image(); + img.decoding = 'async'; + img.src = src; + await img.decode(); + const c = document.createElement('canvas'); + c.width = img.naturalWidth; + c.height = img.naturalHeight; + const ctx = c.getContext('2d', { willReadFrequently: true }); + if (!ctx) throw new Error('2d context unavailable'); + ctx.drawImage(img, 0, 0); + return ctx.getImageData(0, 0, c.width, c.height); +} + +type Panel = { canvas: HTMLCanvasElement; renderer: PipelinePanelGLRenderer; mode: PanelMode }; + +async function main(): Promise { + const fig = byId('explorable'); + if (!fig) return; + const fallback = byId('exp-fallback'); + const readout = byId('exp-readout'); + + function showFallback(msg?: string): void { + if (fallback) { + fallback.hidden = false; + if (msg) fallback.textContent = msg; + } + const grid = fig!.querySelector('.exp-grid') as HTMLElement | null; + const controls = fig!.querySelector('.exp-controls') as HTMLElement | null; + if (grid) grid.style.display = 'none'; + if (controls) controls.style.display = 'none'; + } + + let pixels: ImageData; + try { + pixels = await loadPixels(SOURCE); + } catch { + showFallback('Could not load the test image.'); + return; + } + + const image = { width: pixels.width, height: pixels.height }; + const nest = NEST ?? centeredNest(image.width, image.height); + const crop = fitCropToNest(image, nest, null); + const geom = buildPanelGeometry(nest, crop); + if (!geom) { + showFallback('That nest is degenerate — pick a smaller rectangle.'); + return; + } + const { ctx, R0 } = geom; + const uRef = panelURef(ctx.rMax); + const lnR0 = Math.log(Math.max(R0, 1e-9)); + + // Source thumbnail + nest overlay. Every cell takes the image's aspect ratio + // (--cell-ar), so the source fills its cell with no letterbox and the nest + // box can be positioned in plain percentages. + fig.style.setProperty('--cell-ar', `${image.width} / ${image.height}`); + const srcImg = byId('exp-src'); + if (srcImg) srcImg.src = SOURCE; + const nestBox = byId('exp-nest'); + if (nestBox) { + nestBox.style.left = `${(nest.x / image.width) * 100}%`; + nestBox.style.top = `${(nest.y / image.height) * 100}%`; + nestBox.style.width = `${(nest.w / image.width) * 100}%`; + nestBox.style.height = `${(nest.h / image.height) * 100}%`; + } + + // GL panels — one WebGL2 context per canvas. Bail to the prose fallback if + // WebGL2 is unavailable (init throws). + const defs: Array<{ id: string; mode: PanelMode }> = [ + { id: 'exp-log', mode: 'log' }, + { id: 'exp-rotlog', mode: 'rotlog' }, + { id: 'exp-escher', mode: 'escher' } + ]; + const panels: Panel[] = []; + try { + for (const d of defs) { + const canvas = byId(d.id); + if (!canvas) continue; + const renderer = new PipelinePanelGLRenderer(); + renderer.init(canvas); + panels.push({ canvas, renderer, mode: d.mode }); + } + } catch { + for (const p of panels) p.renderer.dispose(); + showFallback(); + return; + } + + const pan = { u: 0, v: 0 }; + + function renderPanel(p: Panel): void { + const dpr = window.devicePixelRatio || 1; + const r = p.canvas.getBoundingClientRect(); + if (r.width === 0 || r.height === 0) return; + let W = Math.round(r.width * dpr); + let H = Math.round(r.height * dpr); + const long = Math.max(W, H); + if (long > MAX_PX) { + const s = MAX_PX / long; + W = Math.max(1, Math.round(W * s)); + H = Math.max(1, Math.round(H * s)); + } + if (p.mode === 'escher') { + p.renderer.render({ + pixels, ctx, mode: 'escher', W, H, + scale: W / ctx.W, lnR0, panU: pan.u, panV: pan.v + }); + } else { + p.renderer.render({ + pixels, ctx, mode: p.mode, W, H, + pxPerUnit: panelPxPerUnit(p.mode, ctx.logS, H), uRef, panU: pan.u, panV: pan.v + }); + } + } + + function updateReadout(): void { + if (!readout) return; + if (pan.u === 0 && pan.v === 0) { + readout.textContent = 'drag the log panel — ↔ zoom, ↕ rotate'; + return; + } + const zoom = Math.exp(pan.u); + let deg = ((pan.v * 180) / Math.PI) % 360; + if (deg < 0) deg += 360; + readout.textContent = `u-pan → zoom ×${zoom.toFixed(2)} · v-pan → rotation ${deg.toFixed(0)}°`; + } + + let raf = 0; + function scheduleRender(): void { + if (raf) return; + raf = requestAnimationFrame(() => { + raf = 0; + for (const p of panels) renderPanel(p); + updateReadout(); + }); + } + + // Drag-to-pan: Δx → u (zoom), Δy → v (rotation). One cell-height of vertical + // drag = 2π = exactly one full turn, so the gesture maps 1:1 to the angle. + function attachPan(canvas: HTMLCanvasElement): void { + let active = false; + let lastX = 0; + let lastY = 0; + canvas.addEventListener('pointerdown', (e) => { + active = true; + lastX = e.clientX; + lastY = e.clientY; + try { + canvas.setPointerCapture(e.pointerId); + } catch { + /* pointer not capturable (e.g. synthetic event) */ + } + e.preventDefault(); + }); + canvas.addEventListener('pointermove', (e) => { + if (!active) return; + const h = canvas.getBoundingClientRect().height || 1; + const perUnit = h / TWO_PI; // css px per log-space unit + pan.u += (e.clientX - lastX) / perUnit; + pan.v += (e.clientY - lastY) / perUnit; + lastX = e.clientX; + lastY = e.clientY; + scheduleRender(); + }); + const end = (e: PointerEvent) => { + active = false; + try { + canvas.releasePointerCapture(e.pointerId); + } catch { + /* pointer already released */ + } + }; + canvas.addEventListener('pointerup', end); + canvas.addEventListener('pointercancel', end); + } + const logCanvas = byId('exp-log'); + const rotCanvas = byId('exp-rotlog'); + if (logCanvas) attachPan(logCanvas); + if (rotCanvas) attachPan(rotCanvas); + + byId('exp-reset')?.addEventListener('click', () => { + pan.u = 0; + pan.v = 0; + scheduleRender(); + }); + + const ro = new ResizeObserver(() => scheduleRender()); + ro.observe(fig); + + scheduleRender(); +} + +void main(); diff --git a/vite.config.ts b/vite.config.ts index 28c1a04..572c7ae 100644 --- a/vite.config.ts +++ b/vite.config.ts @@ -130,5 +130,16 @@ export default defineConfig({ // (root, subdirectory, or static-file hosts like GitHub Pages). base: './', plugins: [svelte(), falUpscaleProxy(), generateVariantPages()], + build: { + rollupOptions: { + input: { + // The app, and the standalone explorable explainer (explain.html + + // src/explain/main.ts). Two HTML entry points → dist/index.html and + // dist/explain.html, each with its own bundled module. + main: resolve(process.cwd(), 'index.html'), + explain: resolve(process.cwd(), 'explain.html') + } + } + }, server: { host: '127.0.0.1', port: 5173, strictPort: true } }); From 2f8ab184a9b03cf9b0221504aa55558b656ca1a6 Mon Sep 17 00:00:00 2001 From: Silvio Tomatis Date: Fri, 29 May 2026 09:15:27 +0200 Subject: [PATCH 4/7] docs: add explorable screenshot for the PR Co-Authored-By: Claude Opus 4.8 --- docs/screenshots/explorable.png | Bin 0 -> 396569 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 docs/screenshots/explorable.png diff --git a/docs/screenshots/explorable.png b/docs/screenshots/explorable.png new file mode 100644 index 0000000000000000000000000000000000000000..35810d01647e88216aa4e6a384d164ec503411f8 GIT binary patch literal 396569 zcmYhCWl$Wzl7Mk{cL^>*f_rcX5+K24aar8m-66O;EFRoFKyY_h+}(Y-ysCRw_hbG{ z^>j~7O?CHt(;cazEQ^jpf&v8vg)T2Ar3M8B5+Z* 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zc9j0*(u~KD6k`Ke{TNH5|0H~)3O+C}LnS|dcwgykAh5k`yq#zrO>U<8@o88Z&1x!?~&! zAXhgLRnQ=xYw(w@t`Idg!1Kfl2*t~C186~sslJ1+1@rsX{{7PGzKZkb284R<5Y&uf y@%LH8IRbkFzrOdMudlG}9@Oth@c%jsP!OEVdGQ*@tMu;`5OHB?p-KT=zyAlAzXwYI diff --git a/explain.html b/explain.html index 252b194..d1d0845 100644 --- a/explain.html +++ b/explain.html @@ -4,7 +4,7 @@ What is a tententoon? - + @@ -195,8 +195,8 @@ color: var(--muted); text-align: center; } + figcaption em { font-style: italic; } .fig-droste { max-width: 560px; margin-left: auto; margin-right: auto; } - .fig-spiral { max-width: 380px; margin-left: auto; margin-right: auto; } .pull { font-size: 27px; @@ -209,15 +209,22 @@ } .pull b { color: var(--accent-deep); font-style: italic; } - .steps { margin: 1.5em 0; padding-left: 1.35em; } - .steps li { margin: 0.9em 0; line-height: 1.55; padding-left: 0.25em; } - .steps li::marker { color: var(--accent); font-weight: 700; } - .steps em { font-style: italic; } - .steps sup { font-size: 0.72em; } + /* ── Live panels (src/explain/main.ts) ───────────────────────────────── */ + .panel-cell { + position: relative; + background: #000; + border-radius: 6px; + overflow: hidden; + } + .panel-cell canvas { display: block; width: 100%; height: 100%; } + .ar-img { aspect-ratio: var(--cell-ar, 4 / 3); } + .ar-wide { aspect-ratio: 18 / 7; } - /* ── Live explorable (src/explain/main.ts) ───────────────────────────── */ - .explorable { margin: 1.6em 0 0.4em; } - .exp-grid { + .solo-panel { margin: 2em auto; max-width: 520px; } + .solo-panel .panel-cell { box-shadow: 0 14px 38px rgba(20, 14, 10, 0.2); } + + .experiment { margin: 1.6em 0 0; } + .exp-pair { display: grid; grid-template-columns: 1fr 1fr; gap: 8px; @@ -226,24 +233,10 @@ border-radius: 11px; box-shadow: 0 14px 38px rgba(20, 14, 10, 0.18); } - .exp-grid .cell { - position: relative; - aspect-ratio: var(--cell-ar, 4 / 3); - background: #000; - border-radius: 5px; - overflow: hidden; - } - .exp-grid canvas { display: block; width: 100%; height: 100%; } - .exp-grid .src-wrap { position: absolute; inset: 0; } - .exp-grid .src-wrap img { width: 100%; height: 100%; object-fit: fill; display: block; } - .exp-grid .nest { - position: absolute; - border: 2px solid var(--accent); - box-shadow: 0 0 0 4000px rgba(0, 0, 0, 0.22); - pointer-events: none; - } - #exp-log, #exp-rotlog { cursor: grab; touch-action: none; } - #exp-log:active, #exp-rotlog:active { cursor: grabbing; } + #exp-orig { will-change: transform; } + #exp-log { cursor: grab; touch-action: none; } + #exp-log:active { cursor: grabbing; } + .plabel { position: absolute; left: 7px; @@ -289,7 +282,7 @@ align-items: center; justify-content: space-between; gap: 12px; - margin-top: 9px; + margin: 9px 0 0.4em; font-family: Inter, system-ui, sans-serif; font-size: 13px; color: var(--ink-2); @@ -305,6 +298,7 @@ border-radius: 7px; padding: 5px 13px; cursor: pointer; + flex-shrink: 0; } .exp-controls button:hover { border-color: var(--accent); color: var(--accent); } .exp-fallback { font-family: Inter, system-ui, sans-serif; font-size: 13.5px; color: var(--muted); } @@ -362,7 +356,7 @@

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zc9j0*(u~KD6k`Ke{TNH5|0H~)3O+C}LnS|dcwgykAh5k`yq#zrO>U<8@o88Z&1x!?~&! zAXhgLRnQ=xYw(w@t`Idg!1Kfl2*t~C186~sslJ1+1@rsX{{7PGzKZkb284R<5Y&uf y@%LH8IRbkFzrOdMudlG}9@Oth@c%jsP!OEVdGQ*@tMu;`5OHB?p-KT=zyAlAzXwYI literal 0 HcmV?d00001 From c83e0cef38f8894407f890297c698749269cfa37 Mon Sep 17 00:00:00 2001 From: Silvio Tomatis Date: Fri, 29 May 2026 09:29:47 +0200 Subject: [PATCH 5/7] feat(explain): distribute the live panels; drag-the-log experiment Per feedback, drop the 2x2 grid and the source panel. The tententoon spiral now replaces the animated GIF in 'Now bend it'. In 'Why doesn't it tear?', the log(z-c) panel becomes a hands-on experiment: drag it and the original picture beside it rotates (vertical) and zooms (horizontal), with a live readout. The rotated-log lattice stands on its own as the 'lean it over' illustration. 'The original' is rendered by the same engine with the twist off (kTwist=0), so it zooms cleanly (mipmapped) and seamlessly. Verified: vertical drag -> 144 deg rotation, horizontal -> x33 zoom. Co-Authored-By: Claude Opus 4.8 --- docs/screenshots/explorable.png | Bin 396569 -> 185883 bytes explain.html | 196 +++++++++++++------------------- src/explain/main.ts | 118 +++++++++---------- 3 files changed, 137 insertions(+), 177 deletions(-) diff --git a/docs/screenshots/explorable.png b/docs/screenshots/explorable.png index 35810d01647e88216aa4e6a384d164ec503411f8..9938e668d9c982769ab3910d412fcacd6395aeb4 100644 GIT binary patch literal 185883 zcmY&Tvvo-FEySoG@xH}0>fZ*;9!FBOPLjnYM0&H-1ch|)of-UY2FR$MBtM9$4 zTT}O+xplgy?@agUInnB>3IH@xG#D5dz~@i0UtnP10{*?^pznIDf98dY!3d zoBy9#uK)9qggdmp3-r!^545by&!RTJd}BWLh@&g;`R=spF{8@&GJ**5e`gHc9$F*> zt~Ld(K3*R@>Lk4TzV%VP)dBaXM5mkoKP=Zka!&Q~JY%Vmt13$DF*%L)-OP=ewzjhW zjomfSkW;;C^JZcbqm&Sz!>?81CQRZX$Gc16|Je9M<=XLVbPlJDE^+9<8T1eB7CPl` zW{Lmh2Z=LM45arrh4+s4eF5=X^sWnZ=zn|X|JjMW_+DMcHWo|7iPUwY)aCI$b?WFM z;p=uWJy0R2x^dl`t#@YPcQ`{G(@X8BWu&96xfpUTr(rm+O)MV-)Ag84e!6?#z#X6e zPSza9BQ}q5yv}S}Kf`%a6?82&)%8}9i;JK^9672vZECcrpH3fhT#Q+;bS-N8m86i5 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