Clyune Component GallerySierpinski Triangle · How it works & code
Connect a triangle to the middle of the three sides. Dig the middle one 3 Small triangles; repeat each.
Runtime logic
Visiting `/generative/sierpinski`, DemoHost lazy-loads `demos/kits/kit-generative.js` (registry `mod: 'kit-generative'`) and calls `mount(host, { variant: 'sierpinski' })`. mount resolves the variant to family `sierpinski`; `withControls` builds the control panel (6 presets + sliders). `createCanvasStage` creates the `<canvas>` (HiDPI ≤ 2×, ResizeObserver) and the info panel. The family’s `build(S)` initialises state and returns the per-frame callback. Every `requestAnimationFrame`: read controls, advance a speed-scaled clock (dt ≤ 50 ms), run the frame callback; returned readouts go to the info panel. Changing parameters: colour/speed/size apply live; structural ones remount; leaving the page cancels rAF, removes listeners and frees resources.
Environment
Canvas 2D: 2D canvas drawing; requestAnimationFrame: Display-synced animation loop; ResizeObserver: Canvas follows container size; Pointer Events: Unified mouse/touch/pen events; devicePixelRatio: Crisp HiDPI rendering (capped at 2×) · react 18.3.1, react-router-dom 6.30.6, vite 5.4.21
Dependencies
react 18.3.1
Imported APIs
withControls — Wraps the demo in the shared control panel (presets, sliders, reset); hot-updates or remounts on change; paramsFromSpec — Turns the spec (colour/speed/size/count/extras) into control-panel parameter definitions; createCanvasStage — Shared Canvas 2D stage: canvas + info panel, HiDPI, one rAF loop, pointer state, idle auto-pointer; hueOf — Hue of a colour (0–360°); clamp — Clamps a value to a range; TAU — Constant 2π; fmt — Number formatting (fixed decimals); F — Formula block HTML; S.clear — Clears with the background colour (translucent = trails); S.onFrame — Registers a per-frame callback; its return value feeds the info panel; ctx.beginPath() — Starts a new path; ctx.moveTo() — Moves the pen without drawing; ctx.lineTo() — Adds a straight line to a point; ctx.closePath() — Closes the current sub-path; ctx.fill() — Fills the current path; ctx.stroke() — Strokes the current path; ctx.arcTo() — Adds an arc using tangent lines; ctx.fillRect() — Fills a rectangle; ctx.arc() — Adds a circular arc (center, radius, start/end angle); ctx.drawImage() — Draws an image or offscreen canvas; ctx.save() — Saves the drawing state (transform, styles, clip); ctx.rect() — Adds a rectangle to the path; ctx.clip() — Turns the current path into the clipping region; ctx.restore() — Restores the saved drawing state
Source code
frontend/src/demos/kits/kit-generative.js: FAM.sierpinski (L238-L257)
Code walkthrough
L238-257: Calls the factory `gFam()` to produce the full definition (spec + doc + build) from the options below. L238-238: Title shown in the info and control panels: “Sierpinski Triangle”. L238-238: Range/default of the size slider: Stroke Width. L238-238: Range/default of the count slider: Recursion Level. L239-239: Extra demo-specific slider/toggle: Fill. L239-239: Default main colour. L239-239: Help text of the count parameter. L239-239: Preset buttons: name → parameter overrides (4). L240-240: Body of the “Notes” section. L240-240: Main formula of the “Formula” section. L240-240: Second formula line. L241-257: Per-frame draw function: draws with Canvas 2D `beginPath`, `moveTo`, `lineTo`, `closePath`, `fill`, `stroke`; math via `Math.min`, `Math.sin`, `Math.cos`; returns readouts `mode`, `cell` to the info panel.
Principles
第 n Layer triangles = 3ⁿ Area share = (3/4)ⁿ → 0 (Fractal dimensions log3/log2 ≈ 1.585) Sierpinski 三角：把一个三角形三条边的中点连起来，挖掉中间那个，剩下 3 个小三角；再对每个小三角重复。层数越多越像「镂空」。每层会轻轻呼吸缩放，指针所在的小三角会被高亮。 Generative Art = a simple mathematical rule + Random number/噪声，让电脑自己「画」出图案；改变参数就是改变规则。