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The // discharge channel is a perfect conductor held at phi = 0; the left and // right plates are held at phi = 1; top and bottom are insulating (Neumann, // mirrored rows), which is what makes the figure spread ACROSS the frame // instead of sprinting for whichever edge happens to be nearest. Each frame // runs 12 Gauss-Seidel sweeps of the 5-point Laplace stencil over the // aggregate's bounding box (the far field is flat at 1, so relaxing outside // it buys nothing), then grows the tree one site at a time by drawing a // candidate — an unoccupied 4-neighbour of the aggregate — with probability // proportional to phi_i^eta. Growth is held PLATE_CLEARANCE columns clear of // the two plates; see that constant for why. // // eta is the whole character of the piece. At eta = 1 this is a fat DLA blob; // at eta = 3 the tip with the steepest local field wins almost every draw, so // the aggregate collapses into a few long, sharply forked channels covering // ~3% of the grid and leaving the rest of the frame black. That sparsity is // structural, not a threshold applied afterwards. // // Glyphs are chosen by BRANCH GEOMETRY rather than luminance: the two-link // chord from a cell's grandparent gives '-', '|', '/' or '\', and any cell // that acquires a second child becomes '+', the fork. The tree therefore // reads as drawn line-work. Brightness is pow(1 - depth/maxDepth, 0.7), so // the trunk near the seed is hot and the fine tips are faint, which is what a // discharge photograph actually looks like. // // The pointer is an electrode. Cells within 6 of it are pinned above plate // potential on a gaussian profile, eased in over tau 0.45s; because the // growth weight goes as phi^3, the Laplace solution steepens toward it and // new branches visibly fork and race for the cursor. On leave the pin eases // back out and later branching returns to its undisturbed statistics. // Already-grown channel stays exactly where it is: a discharge does not // un-happen. // // The optional `quiet` rect is a patch of dielectric held at lower field // strength: its scale multiplies the growth weight, so fewer channels grow // there and the figure thins out to nothing across the falloff band. Overlaid // copy therefore reads against bare background without a scrim over the field. // --------------------------------------------------------------------------- /** '-' horizontal link, '|' vertical, '/' and '\' the two diagonals, '+' a fork */ const GLYPHS = ["-", "|", "/", "\\", "+"] as const; const BUCKETS = 6; // alpha buckets — one ctx.globalAlpha write each, never per cell const SWEEPS = 12; // Gauss-Seidel sweeps per animated frame const PRIME_SWEEPS = 2; // sweeps per site when a figure is built in one go const PRIME_WARMUP = 40; // sweeps before the first site of a primed figure const GROW_MS = 2200; // a figure completes in ~2.2s const PERIOD_MS = 3600; // a new strike is seeded every 3.6s const FADE_DELAY_MS = 4900; // ...and starts fading only once its successor is well under way const FADE_MS = 1600; // ~0.6 alpha/s const SITES_PER_COL = 3.2; // budget tied to width, because the figure must span it const MIN_SITES = 160; const MAX_SITES = 1000; const RELAX_MARGIN = 14; // cells of slack around the aggregate bbox // Columns 0 and cols-1 are the plates: the relaxation never writes them, so // they hold phi = 1 forever. A cell at x = 1 therefore always has a // full-strength source as a neighbour, and once the channel touched the plate // it ran straight down it — a dead-straight 1-cell rule glued to the frame // edge that took ~11% of the figure's sites (measured, both plates). Growth is // kept this many columns clear of the plates, which drops that to ~4% and // leaves the branch that gets there reading as a trunk rather than a border. // x only: the top and bottom rows ARE written, by the Neumann mirror, so they // are not sources and a y clearance would cost vertical span for nothing. const PLATE_CLEARANCE = 10; // columns const ELECTRODE_R = 6; // cells const ELECTRODE_SIGMA2 = 18; const ELECTRODE_GAIN = 0.9; const ELECTRODE_TAU = 0.45; // s const DT_MAX = 0.05; /** deterministic PRNG — a session replays identically, unlike Math.random */ function mulberry32(seed: number) { let a = seed >>> 0; return () => { a = (a + 0x6d2b79f5) >>> 0; let t = a; t = Math.imul(t ^ (t >>> 15), t | 1); t ^= t + Math.imul(t ^ (t >>> 7), t | 61); return ((t ^ (t >>> 14)) >>> 0) / 4294967296; }; } interface Strike { occupied: Uint8Array; parent: Int32Array; candParent: Int32Array; depth: Uint16Array; kids: Uint8Array; glyph: Uint8Array; order: Int32Array; isCand: Uint8Array; cands: number[]; count: number; maxDepth: number; born: number; // seconds, on the loop clock done: boolean; minX: number; maxX: number; minY: number; maxY: number; } export interface StrikeFigureProps { /** grid cell size in px */ cellSize?: number; /** DBM growth exponent — 1 is a fat blob, 3 the sparse forked lightning figure */ eta?: number; /** * Rect of lowered field strength in normalized frame coords (0..1 from the * top-left) — pass the rect the overlaid copy occupies. Growth weight is * scaled to zero inside it and ramps back to full just outside, so the * discharge grows fewer channels there instead of being masked afterwards. */ quiet?: { x: number; y: number; w: number; h: number }; /** copy overlaid on the discharge; also informs the `quiet` rect's contents */ children?: ReactNode; /** extra classes merged onto the rendered root element */ className?: string; } export function StrikeFigure({ cellSize = 12, eta = 3.0, quiet, children, className = "", }: StrikeFigureProps) { // primitives, not the object: an inline literal from the parent would // otherwise be a fresh identity every render and rebuild the whole figure const qx = quiet ? quiet.x : 0; const qy = quiet ? quiet.y : 0; const qw = quiet ? quiet.w : 0; const qh = quiet ? quiet.h : 0; const rootRef = useRef(null); const canvasRef = useRef(null); useEffect(() => { const root = rootRef.current; const canvas = canvasRef.current; if (!root || !canvas) return; const ctx = canvas.getContext("2d"); if (!ctx) return; const reduced = window.matchMedia("(prefers-reduced-motion: reduce)").matches; let fg = "currentColor"; let accent = "currentColor"; let cellW = cellSize; let cellH = cellSize; let cols = 0; let rows = 0; let target = 0; let keep = 1; // resolved plate clearance, clamped to the grid in rebuild() let sized = false; let disposed = false; let phi = new Float32Array(0); // per-cell field scale: 1 everywhere by default, 0 inside the quiet rect, // smoothstepped back up across the falloff band so there is no contour let quietMask: Float32Array | null = null; let pool: Strike[] = []; let live: Strike[] = []; let poolCursor = 0; let rng = mulberry32(0x1ec47); let seedFlip = 0; let nextBirth = 0; const bucketLists: number[][] = Array.from({ length: BUCKETS }, () => []); // -- tokens --------------------------------------------------------------- const readTokens = () => { fg = getComputedStyle(canvas).color; const raw = getComputedStyle(document.documentElement) .getPropertyValue("--ns-accent") .trim(); accent = raw || fg; }; // -- geometry ------------------------------------------------------------- const makeStrike = (): Strike => { const n = cols * rows; return { occupied: new Uint8Array(n), parent: new Int32Array(n), candParent: new Int32Array(n), depth: new Uint16Array(n), kids: new Uint8Array(n), glyph: new Uint8Array(n), order: new Int32Array(target), isCand: new Uint8Array(n), cands: [], count: 0, maxDepth: 1, born: 0, done: false, minX: 0, maxX: 0, minY: 0, maxY: 0, }; }; // -- field ---------------------------------------------------------------- // Dirichlet phi = 1 on the left and right plates (columns 0 and cols-1), // Neumann on top and bottom, phi = 0 inside the channel. const resetField = () => { phi.fill(1); }; /** * A region of the dielectric held at lower field strength grows fewer * channels — that is all this is. The scale multiplies the growth weight, * so the tree thins out and stops at the edge of the rect on its own * rather than being covered up after the fact. */ const buildQuietMask = () => { if (qw <= 0 || qh <= 0) { quietMask = null; return; } const x0 = qx * cols; const x1 = (qx + qw) * cols; const y0 = qy * rows; const y1 = (qy + qh) * rows; // the falloff band, 5% of the frame width and never under 2 cells: a // hard edge would read as the panel this whole approach exists to avoid const band = Math.max(2, 0.05 * cols); const m = new Float32Array(cols * rows); for (let y = 0; y < rows; y++) { const dy = y < y0 ? y0 - y : y > y1 ? y - y1 : 0; for (let x = 0; x < cols; x++) { const dx = x < x0 ? x0 - x : x > x1 ? x - x1 : 0; const d = Math.sqrt(dx * dx + dy * dy) / band; const f = d < 1 ? d : 1; m[y * cols + x] = f * f * (3 - 2 * f); // smoothstep } } quietMask = m; }; const electrode = { gx: -1e5, gy: -1e5, has: false, strength: 0 }; const pinElectrode = () => { if (electrode.strength <= 0.01) return; const ex = electrode.gx; const ey = electrode.gy; const s = live[live.length - 1]; if (!s) return; const x0 = Math.max(1, Math.floor(ex - ELECTRODE_R)); const x1 = Math.min(cols - 2, Math.ceil(ex + ELECTRODE_R)); const y0 = Math.max(1, Math.floor(ey - ELECTRODE_R)); const y1 = Math.min(rows - 2, Math.ceil(ey + ELECTRODE_R)); const r2 = ELECTRODE_R * ELECTRODE_R; for (let y = y0; y <= y1; y++) { const row = y * cols; for (let x = x0; x <= x1; x++) { const dx = x - ex; const dy = y - ey; const d2 = dx * dx + dy * dy; if (d2 > r2) continue; const i = row + x; if (s.occupied[i]) continue; phi[i] = 1 + ELECTRODE_GAIN * Math.exp(-d2 / ELECTRODE_SIGMA2) * electrode.strength; } } }; const relax = (sweeps: number, s: Strike) => { let x0 = Math.max(1, s.minX - RELAX_MARGIN); let x1 = Math.min(cols - 2, s.maxX + RELAX_MARGIN); let y0 = Math.max(1, s.minY - RELAX_MARGIN); let y1 = Math.min(rows - 2, s.maxY + RELAX_MARGIN); if (electrode.strength > 0.01) { x0 = Math.max(1, Math.min(x0, Math.floor(electrode.gx - ELECTRODE_R - 2))); x1 = Math.min(cols - 2, Math.max(x1, Math.ceil(electrode.gx + ELECTRODE_R + 2))); y0 = Math.max(1, Math.min(y0, Math.floor(electrode.gy - ELECTRODE_R - 2))); y1 = Math.min(rows - 2, Math.max(y1, Math.ceil(electrode.gy + ELECTRODE_R + 2))); } if (x1 < x0 || y1 < y0) return; const occ = s.occupied; for (let k = 0; k < sweeps; k++) { for (let y = y0; y <= y1; y++) { const row = y * cols; for (let x = x0; x <= x1; x++) { const i = row + x; if (occ[i]) { phi[i] = 0; continue; } phi[i] = 0.25 * (phi[i - 1] + phi[i + 1] + phi[i - cols] + phi[i + cols]); } } // insulating top/bottom: the ghost row mirrors its neighbour if (y0 <= 1) { for (let x = x0; x <= x1; x++) phi[x] = phi[cols + x]; } if (y1 >= rows - 2) { const a = (rows - 1) * cols; const b = (rows - 2) * cols; for (let x = x0; x <= x1; x++) phi[a + x] = phi[b + x]; } pinElectrode(); } }; // -- growth --------------------------------------------------------------- const addCandidate = (s: Strike, i: number, from: number) => { if (s.occupied[i] || s.isCand[i]) return; s.isCand[i] = 1; s.candParent[i] = from; s.cands.push(i); }; const occupy = (s: Strike, i: number, from: number) => { s.occupied[i] = 1; phi[i] = 0; s.parent[i] = from; const x = i % cols; const y = (i - x) / cols; if (s.count === 0) { s.minX = s.maxX = x; s.minY = s.maxY = y; } else { if (x < s.minX) s.minX = x; if (x > s.maxX) s.maxX = x; if (y < s.minY) s.minY = y; if (y > s.maxY) s.maxY = y; } if (from < 0) { s.depth[i] = 0; s.glyph[i] = 4; } else { const d = s.depth[from]! + 1; s.depth[i] = d; if (d > s.maxDepth) s.maxDepth = d; s.kids[from] = (s.kids[from]! + 1) as number; if (s.kids[from]! >= 2) s.glyph[from] = 4; // this cell forked // glyph from the two-link chord (grandparent -> here), so a staircase // run reads as a diagonal rather than a stack of alternating dashes const gp = s.parent[from]! >= 0 ? s.parent[from]! : from; const gx = gp % cols; const gy = (gp - gx) / cols; const dx = x - gx; const dy = y - gy; const adx = dx < 0 ? -dx : dx; const ady = dy < 0 ? -dy : dy; let g: number; if (adx > 0 && ady > 0) g = dx * dy > 0 ? 3 : 2; else if (adx >= ady) g = 0; else g = 1; s.glyph[i] = g; } s.order[s.count] = i; s.count++; if (y > 1) addCandidate(s, i - cols, i); if (y < rows - 2) addCandidate(s, i + cols, i); if (x > keep) addCandidate(s, i - 1, i); if (x < cols - 1 - keep) addCandidate(s, i + 1, i); }; /** one DBM growth event: draw a candidate with p ∝ phi^eta */ const growOne = (s: Strike): boolean => { const cands = s.cands; const n = cands.length; if (n === 0 || s.count >= target) return false; const q = quietMask; let total = 0; for (let k = 0; k < n; k++) { const c = cands[k]!; const p = phi[c]!; if (p > 0) total += Math.pow(p, eta) * (q ? q[c]! : 1); } let li: number; if (total > 1e-12) { const r = rng() * total; let acc = 0; li = n - 1; for (let k = 0; k < n; k++) { const c = cands[k]!; const p = phi[c]!; if (p > 0) acc += Math.pow(p, eta) * (q ? q[c]! : 1); if (acc >= r) { li = k; break; } } } else { li = Math.min(n - 1, Math.floor(rng() * n)); } const pick = cands[li]!; cands[li] = cands[n - 1]!; cands.pop(); s.isCand[pick] = 0; occupy(s, pick, s.candParent[pick]!); return true; }; const seedStrike = (s: Strike, t: number) => { s.occupied.fill(0); s.isCand.fill(0); s.kids.fill(0); s.cands.length = 0; s.count = 0; s.maxDepth = 1; s.done = false; s.born = t; resetField(); // two anchors, alternating, with a jittered offset — successive strikes // land on opposite thirds of the frame const upperLeft = seedFlip % 2 === 0; seedFlip++; const fx = upperLeft ? 0.3 : 0.7; const fy = upperLeft ? 0.34 : 0.66; const jx = (rng() - 0.5) * 0.1 * cols; const jy = (rng() - 0.5) * 0.16 * rows; const sx = Math.min( cols - 2 - keep, Math.max(keep + 1, Math.round(fx * cols + jx)) ); const sy = Math.min(rows - 3, Math.max(2, Math.round(fy * rows + jy))); occupy(s, sy * cols + sx, -1); }; /** build one complete figure in a single blocking pass */ const primeStrike = (s: Strike, t: number) => { seedStrike(s, t); relax(PRIME_WARMUP, s); while (s.count < target) { relax(PRIME_SWEEPS, s); if (!growOne(s)) break; } s.done = true; }; // -- render --------------------------------------------------------------- const strikeAlpha = (s: Strike, t: number) => { const ageMs = (t - s.born) * 1000; if (ageMs <= FADE_DELAY_MS) return 1; return Math.max(0, 1 - (ageMs - FADE_DELAY_MS) / FADE_MS); }; const draw = (t: number) => { if (!sized) return; ctx.clearRect(0, 0, cols * cellW, rows * cellH); for (let b = 0; b < BUCKETS; b++) bucketLists[b]!.length = 0; for (let si = 0; si < live.length; si++) { const s = live[si]!; const a = strikeAlpha(s, t); if (a <= 0.01) continue; const md = Math.max(4, s.maxDepth); for (let k = 0; k < s.count; k++) { const idx = s.order[k]!; const rel = 1 - s.depth[idx]! / md; const lum = Math.pow(rel > 0.08 ? rel : 0.08, 0.7) * a; let b = Math.floor(lum * BUCKETS); if (b < 0) b = 0; else if (b > BUCKETS - 1) b = BUCKETS - 1; bucketLists[b]!.push(idx * 5 + s.glyph[idx]!); } } for (let b = 0; b < BUCKETS; b++) { const list = bucketLists[b]!; if (list.length === 0) continue; ctx.globalAlpha = 0.1 + (b / (BUCKETS - 1)) * 0.9; // the hot core of the channel carries the one accent; everything else // is monochrome ink ctx.fillStyle = b === BUCKETS - 1 ? accent : fg; for (let k = 0; k < list.length; k++) { const v = list[k]!; const g = v % 5; const idx = (v - g) / 5; const gx = idx % cols; const gy = (idx - gx) / cols; ctx.fillText( GLYPHS[g]!, gx * cellW + cellW / 2, gy * cellH + cellH / 2 ); } } ctx.globalAlpha = 1; }; // -- sizing --------------------------------------------------------------- const measureCell = (fontFamily: string) => { const off = document.createElement("canvas"); const octx = off.getContext("2d"); if (!octx) return; octx.font = `${cellSize}px ${fontFamily}`; cellW = Math.max(4, octx.measureText("MMMMMMMMMM").width / 10); cellH = cellSize; }; const rebuild = (t: number) => { const { width, height } = canvas.getBoundingClientRect(); if (width < 2 || height < 2) { sized = false; return; } const dpr = Math.min(window.devicePixelRatio || 1, 2); canvas.width = Math.max(1, Math.round(width * dpr)); canvas.height = Math.max(1, Math.round(height * dpr)); ctx.setTransform(dpr, 0, 0, dpr, 0, 0); const fontFamily = getComputedStyle(canvas).fontFamily; measureCell(fontFamily); ctx.font = `${cellSize}px ${fontFamily}`; ctx.textAlign = "center"; ctx.textBaseline = "middle"; cols = Math.max(12, Math.ceil(width / cellW)); rows = Math.max(12, Math.ceil(height / cellH)); // a narrow grid must still leave room to grow between the two clearances keep = Math.max(1, Math.min(PLATE_CLEARANCE, Math.floor(cols / 6))); target = Math.max( MIN_SITES, Math.min(MAX_SITES, Math.round(cols * SITES_PER_COL)) ); phi = new Float32Array(cols * rows); buildQuietMask(); rng = mulberry32(0x1ec47); seedFlip = 0; pool = [makeStrike(), makeStrike()]; poolCursor = 0; live = []; sized = true; // the frame is never allowed to open empty: the first figure is built // complete, then back-dated so it is already in its hold phase const first = pool[0]!; poolCursor = 1; primeStrike(first, t - GROW_MS / 1000); live = [first]; nextBirth = first.born + PERIOD_MS / 1000; draw(t); }; // -- loop ----------------------------------------------------------------- let raf = 0; let last = 0; let clock = 0; const step = (dt: number) => { clock += dt; const t = clock; const want = electrode.has ? 1 : 0; electrode.strength += (want - electrode.strength) * Math.min(1, dt / ELECTRODE_TAU); // retire dead strikes before spawning, so the pool of two always has a // free slot for (let i = live.length - 1; i >= 0; i--) { if ((t - live[i]!.born) * 1000 > FADE_DELAY_MS + FADE_MS) live.splice(i, 1); } if (t >= nextBirth) { const s = pool[poolCursor % 2]!; poolCursor++; const at = live.indexOf(s); if (at >= 0) live.splice(at, 1); seedStrike(s, t); live.push(s); nextBirth = t + PERIOD_MS / 1000; } const g = live[live.length - 1]; if (g) { if (!g.done) { relax(SWEEPS, g); const wantN = Math.min( target, Math.round((target * ((t - g.born) * 1000)) / GROW_MS) ); let n = wantN - g.count; while (n-- > 0 && growOne(g)) { /* one site per tick */ } if (g.count >= target || g.cands.length === 0) g.done = true; } else if (electrode.strength > 0.01) { // keep the field warm so the electrode is already in the solution // when the next strike seeds relax(2, g); } } draw(t); }; const loop = (now: number) => { const dt = last ? Math.min(DT_MAX, (now - last) / 1000) : 1 / 60; last = now; step(dt); if (!document.hidden) raf = requestAnimationFrame(loop); }; // -- listeners ------------------------------------------------------------ let resizeTimer: ReturnType | null = null; const onResize = () => { if (resizeTimer) clearTimeout(resizeTimer); resizeTimer = setTimeout(() => { resizeTimer = null; rebuild(clock); }, 150); }; const onPointerMove = (e: PointerEvent) => { const rect = canvas.getBoundingClientRect(); electrode.gx = (e.clientX - rect.left) / cellW; electrode.gy = (e.clientY - rect.top) / cellH; electrode.has = true; }; const onPointerLeave = () => { electrode.has = false; }; const onVis = () => { if (!document.hidden && !reduced && sized) { last = 0; raf = requestAnimationFrame(loop); } }; const mo = new MutationObserver(() => { readTokens(); if (reduced) draw(clock); }); mo.observe(document.documentElement, { attributes: true, attributeFilter: ["class"], }); document.fonts.ready.then(() => { if (disposed) return; readTokens(); rebuild(0); if (!reduced) raf = requestAnimationFrame(loop); }); window.addEventListener("resize", onResize); if (!reduced) { root.addEventListener("pointermove", onPointerMove); root.addEventListener("pointerleave", onPointerLeave); } document.addEventListener("visibilitychange", onVis); return () => { disposed = true; cancelAnimationFrame(raf); if (resizeTimer) clearTimeout(resizeTimer); mo.disconnect(); window.removeEventListener("resize", onResize); root.removeEventListener("pointermove", onPointerMove); root.removeEventListener("pointerleave", onPointerLeave); document.removeEventListener("visibilitychange", onVis); }; }, [cellSize, eta, qx, qy, qw, qh]); // `h-full` matters as much as the min-height: a min-height is only a floor, // so a stretched grid/flex parent taller than it would leave a band of dead // background under the field. return (

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