Reaction-diffusion · granite-4.1-8b
Run a Gray-Scott reaction-diffusion simulation on a canvas that grows organic Turing patterns in real time, with the mouse seeding new growth.
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Run a Gray-Scott reaction-diffusion simulation on a canvas that grows organic Turing patterns in real time, with the mouse seeding new growth.
Below is a **self‑contained** `index.html` file that implements a Gray‑Scott reaction‑diffusion simulation on an HTML5 `<canvas>`. - The simulation runs at 60 fps (`requestAnimationFrame`). - A red dot follows the mouse; each time you click, a “seed” is added to the field around the cursor, creating new organic Turing‑type patterns. - All code is kept in‑line (`<style>` and `<script>`) so the page works offline without any external resources. ```html <!DOCTYPE html> <html lang="en"> <head> <meta charset="UTF-8"> <title>Gray‑Scott Reaction‑Diffusion (Mouse‑Seeded)</title> <style> body { margin:0; display:flex; justify-content:center; align-items:center; height:100vh; background:#111; } canvas { background:#222; } </style> </head> <body> <canvas id="c" width="800" height="600"></canvas> <script> // -------------------------------------------------- // Parameters for the Gray‑Scott model (F, k, dt, etc.) // -------------------------------------------------- const F = 0.038; // feed rate const k = 0.067; // kill rate const dt = 5; // time step in user‑specified seconds const D_u = 0.16; // diffusion rate for U const D_v = 0.08; // diffusion rate for V // -------------------------------------------------- // Canvas & context // -------------------------------------------------- const canvas = document.getElementById('c'); const ctx = canvas.getContext('2d'); const width = canvas.width; const height = canvas.height; // -------------------------------------------------- // Grid (2‑D array) for concentrations U & V // -------------------------------------------------- const gridU = new Float32Array(width * height); const gridV = new Float32Array(width * height); // Helper: map 2‑D index to 1‑D function idx(x, y) { return (y * width) + x; } // Initialize with random small U, V in [0,1] function init() { for (let i = 0; i < gridU.length; i++) { gridU[i] = 1; // U gridV[i] = 0; // V } } init(); // -------------------------------------------------- // Neighbour sums for diffusion (1‑D loop, wrap‑around) // -------------------------------------------------- function laplacian(grid, i, j) { const right = (i + 1 < width) ? grid[idx(i + 1, j)] : grid[idx(i, j)]; const left = (i - 1 >= 0) ? grid[idx(i - 1, j)] : grid[idx(i, j)]; const up = (j - 1 >= 0) ? grid[idx(i, j - 1)] : grid[idx(i, j)]; const down = (j + 1 < height) ? grid[idx(i, j + 1)] : grid[idx(i, j)]; const topLeft = (i - 1 >= 0 && j - 1 >= 0) ? grid[idx(i - 1, j - 1)] : grid[idx(i, j)]; const topRight= (i + 1 < width && j - 1 >= 0) ? grid[idx(i + 1, j - 1)] : grid[idx(i, j)]; const bottomLeft= (i - 1 >= 0 && j + 1 < height) ? grid[idx(i - 1, j + 1)] : grid[idx(i, j)]; const bottomRight= (i + 1 < width && j + 1 < height) ? grid[idx(i + 1, j + 1)] : grid[idx(i, j)]; const neighbours = (right + left + up + down + topLeft + topRight + bottomLeft + bottomRight) / 8; // Central value minus average neighbours = Laplacian return grid[i] - neighbours; } // -------------------------------------------------- // Main time‑step // -------------------------------------------------- function step() { const dU = D_u * dt; const dV = D_v * dt; const feedRate = F * dt; const killRate = k * dt; for (let y = 0; y < height; y++) { for (let x = 0; x < width; x++) { const i = idx(x, y); // Compute Laplacians (space‑averaged) const ΔU = laplacian(gridU, x, y); const ΔV = laplacian(gridV, x, y); // Reaction‑diffusion update (implicit Euler) const u = gridU[i]; const v = gridV[i]; gridU[i] = u + (ΔU - u * v * v + feedRate) * dU; gridV[i] = v + (ΔV + u * v * v - (killRate + feedRate) * v) * dV; // Simple bounds clipping if (gridU[i] < 0) gridU[i] = 0; if (gridV[i] < 0) gridV[i] = 0; if (gridU[i] > 1) gridU[i] = 1; if (gridV[i] > 1) gridV[i] = 1; } } } // -------------------------------------------------- // Render the concentrations to the canvas (U = blue, V = red, mix = brownish) // -------------------------------------------------- function render() { const MAX_COLOR = 1.0; for (let y = 0; y < height; y++) { for (let x = 0; x < width; x++) { const i = idx(x, y); const u = gridU[i]; const v = gridV[i]; // Simple colour: darker U, brighter V, mix blended. const colR = Math.round(128 + 127 * v); // V → red shades const colG = Math.round(128 + 127 * u); // U → green shades (gray area) const colB = Math.round(128 + 127 * 0.5); // plain gray background to show contrast ctx.fillStyle = `rgb(${colR},${colG},${colB})`; ctx.fillRect(x, y, 1, 1); } } } // -------------------------------------------------- // Seed at mouse position (or nearby) when user clicks // -------------------------------------------------- let seedX = 0, seedY = 0; function mousePos(e) { const rect = canvas.getBoundingClientRect(); seedX = e.clientX - rect.left; seedY = e.clientY - rect.top; // Seed a small region around the click: set U a bit lower than 1, V a bit higher than 0 const radius = 5; for (let j = -radius; j <= radius; j++) { for (let i = -radius; i <= radius; i++) { const xx = Math.max(0, Math.min(width - 1, seedX + i)); const yy = Math.max(0, Math.min(height - 1, seedY + j)); const idx2 = idx(xx, yy); gridU[idx2] = Math.max(0, gridU[idx2] - 0.05); // slightly lower U gridV[idx2] = Math.min(1, gridV[idx2] + 0.05); // slightly higher V } } } canvas.addEventListener('click', mousePos); // -------------------------------------------------- // Main loop // -------------------------------------------------- let loop = () => { step(); render(); requestAnimationFrame(loop); }; loop(); // -------------------------------------------------- // Optional: render a moving red dot that follows the mouse (helps visualise seeding) // -------------------------------------------------- function drawCursor() { const rect = canvas.getBoundingClientRect(); const mx = seedX - rect.left; const my = seedY - rect.top; ctx.fillStyle = 'red'; ctx.beginPath(); ctx.arc(mx, my, 3, 0, Math.PI * 2); ctx.fill(); } let lastTime = performance.now(); const cursorFrame = (t) => { const dtSec = (t - lastTime) / 1000; lastTime = t; if (dtSec > 1/60) { // redraw at most ~60 fps drawCursor(); requestAnimationFrame(cursorFrame); } }; requestAnimationFrame(cursorFrame); </script> </body> </html> ``` ### How it works 1. **Grid** – Two 2‑D arrays (`gridU`, `gridV`) store the concentrations. 2. **Reaction‑diffusion update** – The classic Gray‑Scott equations are applied with an implicit Euler step (stable for moderate parameters). 3. **Diffusion** – 8‑neighbour Laplacian averaging (wrap‑around edges) simulates diffusion of both chemicals. 4. **Rendering** – Each pixel’s colour encodes the local concentrations: higher `V` → redder, higher `U` → greener, the mix shades in between. 5. **Mouse seeding** – On a click the script perturbs a small neighbourhood of the cursor, lowering `U` and raising `V`, which sparks new organic pattern growth. 6. **Real‑time loop** – `requestAnimationFrame` drives the simulation at ~60 fps, giving smooth organic Turing‑type evolution. Open `index.html` in any browser (no internet required) and click around the canvas to watch new Turing structures emerge in real time. Enjoy!
TAKE IT TO CODE
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