Clyune Component GalleryCentral Limit Theorem · How it works & code
Dice mean histogram approaches normal
Runtime logic
Visiting `/math/clt`, DemoHost lazy-loads `demos/kits/kit-math.js` (registry `mod: 'kit-math'`) and calls `mount(host, { variant: 'clt' })`. mount resolves the variant to family `clt`; `withControls` builds the control panel (6 presets + sliders). `createInfoPanel` splits the stage into canvas + info panel; `makeCanvas` creates a HiDPI canvas. Every `requestAnimationFrame`: read controls, `drawFamily` runs this demo’s branch, and the info panel readout refreshes. Pointer down/drag/move updates the interaction (drag handles, hover readouts); when untouched and auto-demo is on, the pointer follows a Lissajous path. 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
makeCanvas — Creates an auto-sized canvas; loop — requestAnimationFrame loop (stoppable); bar — Demo control bar; paramsFromSpec — Turns the spec (colour/speed/size/count/extras) into control-panel parameter definitions; readLiveControls — Reads live control values (CSS-variable fallback); localPoint — Event → canvas-local coordinates; withControls — Wraps the demo in the shared control panel (presets, sliders, reset); hot-updates or remounts on change; createInfoPanel — Side/bottom info panel: live readout + formula/notes/params/steps; alignDocParams — Aligns the documented parameters with the actual controls; MATH_DOCS — Formula/notes/params text table for math demos; ctx.fillRect() — Fills a rectangle; ctx.beginPath() — Starts a new path; ctx.arc() — Adds a circular arc (center, radius, start/end angle); ctx.fill() — Fills the current path; ctx.fillText() — Draws filled text
Source code
frontend/src/demos/kits/kit-math.js: FAMILY_CONTROLS['clt'] (L108-L108), drawFamily() · case 'clt' (L628-L628), MATH_DOCS['clt'] (L322-L330)
Code walkthrough
L108-108: This demo's entry in the `FAMILY_CONTROLS` table (control config). L628-628: `case` branch in `drawFamily()`: this demo's per-frame drawing. L322-330: This demo's entry in the `MATH_DOCS` table (info-panel text: formula/notes/params/steps).
Principles
X̄ ~ N(μ, σ² n ) (n Big enough) Dice:μ = 3.5, σ = √(35/12) ≈ 1.708 Rolling dice itself is evenly distributed, but n The secondary result takes an average redrawing of the histogram, which turns into a bell shape; n The bigger, the narrower, the width 1/√n Down.