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al.) through whatever area the copy leaves empty. // Auxin sources are scattered on a jittered grid across the container, then // every source that falls inside a measured content box (headline, subcopy, // CTA row, stat strip — read live via getBoundingClientRect under a // ResizeObserver) is simply never added. Avoidance is therefore a property // of where the sources exist, not a mask or clip-path drawn over the result. // // Each 30Hz tick: a quadtree of current vein tips answers "which sources are // within reach", tips advance one step toward the mean direction of every // source that picked them as nearest, and a second quadtree of sources // answers "which sources just got swallowed" so they can be removed before // the next tick. Kill distance dk = 1.7x the mean source spacing (the grid // cell size); attraction radius = 5x dk; step length = 0.6x dk (always // smaller than dk, so a step can never leap clean over a source without // killing it). rho — how tight the source grid is packed — is the one knob // between a sparse palm-fan network and a dense reticulate mesh. // // Segment width is NOT looked up from a lookup table; it is Murray's law, // maintained incrementally. Every node tracks leafCount = the number of live // terminal tips its subtree currently ends in (1 while it is itself a tip). // Extending a tip in place never changes that count. Only the moment a node // that already has one child grows a SECOND child — an actual fork — does // its count rise, and that rise is walked straight up its ancestor chain. // Width of the segment feeding any node = leafCount^(1/3), so a trunk is // only ever as thick as the tissue still draining through it. // // Committed geometry is batched into eight elements bucketed by that // width (colour is var(--ns-muted) for the four thin buckets, var(--foreground) // for the four thick ones, via `currentColor` on two wrapping s so a theme // switch repaints for free); only the current tick's freshly grown segments // live in a ninth "active tip" path until the next tick folds them in. Once // no source remains reachable the lamina rests, then abscises — the two // wrapping groups' `color` transitions to var(--background), draining the // whole network into the page — and a fresh source scatter begins. // --------------------------------------------------------------------------- interface Box { x: number; y: number; w: number; h: number; } interface Source { x: number; y: number; } interface VNode { x: number; y: number; parent: number; // -1 = seed, enters from the container edge leafCount: number; children: number[]; } interface QPoint { x: number; y: number; id: number; } /** Minimal point quadtree: insert + circular range query. Rebuilt fresh each * tick from whichever point set (tips, or remaining sources) it is asked to * index — cheap at these counts (<=1500 points) and avoids ever having to * remove a point from a persistent tree. */ class Quadtree { private readonly capacity = 8; private points: QPoint[] = []; private divided = false; private nw: Quadtree | null = null; private ne: Quadtree | null = null; private sw: Quadtree | null = null; private se: Quadtree | null = null; constructor(private readonly bx: number, private readonly by: number, private readonly bw: number, private readonly bh: number) {} private contains(p: QPoint): boolean { return p.x >= this.bx && p.x < this.bx + this.bw && p.y >= this.by && p.y < this.by + this.bh; } private intersectsCircle(cx: number, cy: number, r: number): boolean { const nx = Math.max(this.bx, Math.min(cx, this.bx + this.bw)); const ny = Math.max(this.by, Math.min(cy, this.by + this.bh)); const dx = cx - nx; const dy = cy - ny; return dx * dx + dy * dy <= r * r; } private subdivide(): void { const hw = this.bw / 2; const hh = this.bh / 2; this.nw = new Quadtree(this.bx, this.by, hw, hh); this.ne = new Quadtree(this.bx + hw, this.by, hw, hh); this.sw = new Quadtree(this.bx, this.by + hh, hw, hh); this.se = new Quadtree(this.bx + hw, this.by + hh, hw, hh); this.divided = true; } insert(p: QPoint): boolean { if (!this.contains(p)) return false; if (!this.divided && this.points.length < this.capacity) { this.points.push(p); return true; } if (this.bw < 1 || this.bh < 1) { // degenerate leaf — stop subdividing, just accumulate this.points.push(p); return true; } if (!this.divided) this.subdivide(); return ( (this.nw?.insert(p) ?? false) || (this.ne?.insert(p) ?? false) || (this.sw?.insert(p) ?? false) || (this.se?.insert(p) ?? false) ); } queryRadius(cx: number, cy: number, r: number, out: QPoint[]): void { if (!this.intersectsCircle(cx, cy, r)) return; const r2 = r * r; for (const p of this.points) { const dx = p.x - cx; const dy = p.y - cy; if (dx * dx + dy * dy <= r2) out.push(p); } if (this.divided) { this.nw?.queryRadius(cx, cy, r, out); this.ne?.queryRadius(cx, cy, r, out); this.sw?.queryRadius(cx, cy, r, out); this.se?.queryRadius(cx, cy, r, out); } } } 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; }; } const KILL_RATIO = 1.7; // dk = KILL_RATIO * mean source spacing const ATTRACT_RATIO = 5; // di = ATTRACT_RATIO * dk const STEP_RATIO = 0.6; // D = STEP_RATIO * dk — always < dk const BOX_PAD = 22; // px clearance kept around every measured content box const STEP_MS = 1000 / 30; // fixed 30Hz colonisation tick const STAGNANT_LIMIT = 3; // consecutive empty ticks before growth is "done" const MAX_TICKS = 900; // hard safety cap (~30s at 30Hz) const MAX_NODES = 1600; const REST_MS = 3200; // how long a completed lamina rests before it drains const DRAIN_MS = 1500; // colour-drain to --background const W0 = 0.55; // leaf (tip) stroke width in px const BUCKET_WIDTH = [0.55, 0.85, 1.15, 1.5, 1.9, 2.4, 3.0, 3.7]; const BUCKET_OPACITY = [0.3, 0.4, 0.5, 0.6, 0.5, 0.66, 0.82, 1]; const THIN_BUCKETS = 4; // buckets 0..3 render in the --ns-muted group function buildSeeds(w: number, h: number): Source[] { return [ { x: w * 0.14, y: h - 1 }, { x: w * 0.5, y: h - 1 }, { x: w * 0.86, y: h - 1 }, { x: 1, y: h * 0.28 }, { x: 1, y: h * 0.72 }, { x: w - 1, y: h * 0.28 }, { x: w - 1, y: h * 0.72 }, ]; } function insideAnyBox(x: number, y: number, boxes: Box[]): boolean { for (const b of boxes) { if (x >= b.x - BOX_PAD && x <= b.x + b.w + BOX_PAD && y >= b.y - BOX_PAD && y <= b.y + b.h + BOX_PAD) { return true; } } return false; } function buildSources( w: number, h: number, boxes: Box[], targetCount: number, rand: () => number ): { sources: Source[]; meanSpacing: number } { const area = Math.max(1, w * h); const cell = Math.sqrt(area / Math.max(1, targetCount)); const cols = Math.max(1, Math.round(w / cell)); const rows = Math.max(1, Math.round(h / cell)); const cw = w / cols; const ch = h / rows; const sources: Source[] = []; for (let j = 0; j < rows; j++) { for (let i = 0; i < cols; i++) { const x = (i + 0.5) * cw + (rand() - 0.5) * 0.8 * cw; const y = (j + 0.5) * ch + (rand() - 0.5) * 0.8 * ch; if (x < 0 || y < 0 || x > w || y > h) continue; if (insideAnyBox(x, y, boxes)) continue; sources.push({ x, y }); } } return { sources, meanSpacing: (cw + ch) / 2 }; } export interface AuxinCanalProps { /** mono eyebrow line above the headline */ eyebrow?: string; /** display headline, one string per rendered line */ headlineLines?: string[]; /** muted supporting copy under the headline */ subcopy?: string; /** accent primary CTA */ primaryCta?: { label: string; href: string }; /** ghost secondary CTA */ secondaryCta?: { label: string; href: string }; /** three mono stats for the bordered strip below the CTAs */ stats?: { value: string; label: string }[]; /** target auxin source count before content-box exclusion (rho's knob) */ sourceCount?: number; /** extra classes merged onto the rendered root element */ className?: string; } export function AuxinCanal({ eyebrow = "SPACE-COLONISED ROUTING", headlineLines = ["Traffic finds every channel", "your interface leaves open"], subcopy = "Auxin Canal grows a delivery network through whatever capacity the page doesn't use — sources scattered across the empty space, consumed as tips reach them, and widened by Murray's law so trunks earn their thickness from the load they actually carry.", primaryCta = { label: "Read the docs", href: "#docs" }, secondaryCta = { label: "View the API", href: "#api" }, stats = [ { value: "1,200", label: "auxin sources / cycle" }, { value: "1.7×", label: "kill-distance ratio" }, { value: "30Hz", label: "colonisation tick" }, ], sourceCount = 1200, className = "", }: AuxinCanalProps) { const rootRef = useRef(null); const svgRef = useRef(null); const bucketRefs = useRef<(SVGPathElement | null)[]>([]); const activeRef = useRef(null); const [draining, setDraining] = useState(false); const linesKey = headlineLines.join(" "); useEffect(() => { const root = rootRef.current; const svg = svgRef.current; if (!root || !svg) return; const reduced = window.matchMedia("(prefers-reduced-motion: reduce)").matches; const rand = mulberry32(0xa0c1a2); let disposed = false; let w = 0; let h = 0; let sized = false; let nodes: VNode[] = []; let sources: Source[] = []; let dk = 1; let di = 1; let step = 1; let newTickStart = 0; let stagnant = 0; let tickCount = 0; let phase: "grow" | "rest" | "drain" = "grow"; let visible = true; let raf = 0; let acc = 0; let last = 0; let restTimer = 0; let drainTimer = 0; const measureBoxes = (): Box[] => { const rect = root.getBoundingClientRect(); const boxes: Box[] = []; root.querySelectorAll("[data-auxin-box]").forEach((el) => { const r = el.getBoundingClientRect(); if (r.width <= 0 || r.height <= 0) return; boxes.push({ x: r.left - rect.left, y: r.top - rect.top, w: r.width, h: r.height }); }); return boxes; }; const applyD = (idx: number, d: string) => { const el = bucketRefs.current[idx]; if (el) el.setAttribute("d", d); }; const clearPaths = () => { for (let i = 0; i < 8; i++) applyD(i, ""); activeRef.current?.setAttribute("d", ""); }; // -- one node ends a tip's flight; adding a child is where Murray's law // actually happens: extending an existing tip in place costs nothing, // only a genuine fork (a node gaining its SECOND child) raises leafCount, // and that rise is walked straight up the ancestor chain. -------------- const addChild = (parentIdx: number, x: number, y: number): number => { const idx = nodes.length; nodes.push({ x, y, parent: parentIdx, leafCount: 1, children: [] }); const parent = nodes[parentIdx]; if (!parent) return idx; const wasLeaf = parent.children.length === 0; parent.children.push(idx); if (!wasLeaf) { let cur: number = parentIdx; while (cur !== -1) { const n = nodes[cur]; if (!n) break; n.leafCount += 1; cur = n.parent; } } return idx; }; // -- one fixed-length colonisation step: attract every live source to // its nearest reachable tip via a quadtree of nodes, advance every tip // that attracted at least one source, then kill every source a fresh // node lands within dk of via a quadtree of sources. ------------------ const tick = (): boolean => { if (sources.length === 0 || nodes.length >= MAX_NODES) return false; const nodeQT = new Quadtree(-di, -di, w + 2 * di, h + 2 * di); for (let i = 0; i < nodes.length; i++) { const n = nodes[i]; if (n) nodeQT.insert({ x: n.x, y: n.y, id: i }); } const sumX = new Map(); const sumY = new Map(); const buf: QPoint[] = []; for (const s of sources) { buf.length = 0; nodeQT.queryRadius(s.x, s.y, di, buf); if (buf.length === 0) continue; let bestId = -1; let bestD = Infinity; for (const p of buf) { const dx = p.x - s.x; const dy = p.y - s.y; const d = dx * dx + dy * dy; if (d < bestD) { bestD = d; bestId = p.id; } } if (bestId < 0) continue; const node = nodes[bestId]; if (!node) continue; const dx = s.x - node.x; const dy = s.y - node.y; const len = Math.hypot(dx, dy) || 1; sumX.set(bestId, (sumX.get(bestId) ?? 0) + dx / len); sumY.set(bestId, (sumY.get(bestId) ?? 0) + dy / len); } if (sumX.size === 0) return false; newTickStart = nodes.length; for (const [idx, sx] of sumX) { const sy = sumY.get(idx) ?? 0; const len = Math.hypot(sx, sy) || 1; const parent = nodes[idx]; if (!parent) continue; const nx = parent.x + (sx / len) * step; const ny = parent.y + (sy / len) * step; addChild(idx, nx, ny); if (nodes.length >= MAX_NODES) break; } if (nodes.length === newTickStart) return false; const srcQT = new Quadtree(-1, -1, w + 2, h + 2); for (let i = 0; i < sources.length; i++) { const s = sources[i]; if (s) srcQT.insert({ x: s.x, y: s.y, id: i }); } const dead = new Set(); const kbuf: QPoint[] = []; for (let i = newTickStart; i < nodes.length; i++) { const n = nodes[i]; if (!n) continue; kbuf.length = 0; srcQT.queryRadius(n.x, n.y, dk, kbuf); for (const p of kbuf) dead.add(p.id); } if (dead.size > 0) sources = sources.filter((_, i) => !dead.has(i)); return true; }; // -- rebuild the eight committed buckets (everything grown before this // tick) and the one active-tip path (everything grown this tick). Full // rebuild every tick is O(nodes) — trivial at these counts (<=1600). -- const render = () => { let maxLeaf = 1; for (const n of nodes) if (n.leafCount > maxLeaf) maxLeaf = n.leafCount; const maxWidth = W0 * Math.cbrt(maxLeaf); const spans = new Array(8).fill("") as string[]; let activeSpan = ""; for (let i = 0; i < nodes.length; i++) { const n = nodes[i]; if (!n || n.parent === -1) continue; const p = nodes[n.parent]; if (!p) continue; const seg = `M${p.x.toFixed(1)} ${p.y.toFixed(1)}L${n.x.toFixed(1)} ${n.y.toFixed(1)}`; if (i >= newTickStart) { activeSpan += seg; continue; } const width = W0 * Math.cbrt(n.leafCount); const t = maxWidth > W0 ? (width - W0) / (maxWidth - W0) : 0; const bi = Math.min(7, Math.max(0, Math.floor(t * 8))); spans[bi] += seg; } for (let i = 0; i < 8; i++) applyD(i, spans[i] ?? ""); activeRef.current?.setAttribute("d", activeSpan); }; const finishGrowth = () => { phase = "rest"; newTickStart = nodes.length; // fold whatever was still "active" in render(); window.clearTimeout(restTimer); restTimer = window.setTimeout(beginDrain, REST_MS); }; const beginDrain = () => { if (disposed) return; phase = "drain"; setDraining(true); window.clearTimeout(drainTimer); drainTimer = window.setTimeout(resetCycle, DRAIN_MS); }; const resetCycle = () => { if (disposed) return; setDraining(false); clearPaths(); startCycle(); }; const startCycle = () => { window.clearTimeout(restTimer); window.clearTimeout(drainTimer); const rect = root.getBoundingClientRect(); w = rect.width; h = rect.height; if (w < 2 || h < 2) { sized = false; return; } sized = true; const boxes = measureBoxes(); const built = buildSources(w, h, boxes, sourceCount, rand); sources = built.sources; dk = KILL_RATIO * built.meanSpacing; di = ATTRACT_RATIO * dk; step = STEP_RATIO * dk; nodes = buildSeeds(w, h).map((s) => ({ x: s.x, y: s.y, parent: -1, leafCount: 1, children: [] })); newTickStart = nodes.length; stagnant = 0; tickCount = 0; phase = "grow"; if (reduced) { // run the whole cycle to completion synchronously, once, and stop for (let i = 0; i < MAX_TICKS; i++) { const grew = tick(); if (!grew) { stagnant += 1; if (stagnant >= STAGNANT_LIMIT) break; } else { stagnant = 0; } } newTickStart = nodes.length; render(); phase = "rest"; // settled — no drain, no further cycles return; } last = 0; acc = 0; if (!raf) raf = requestAnimationFrame(loop); }; const loop = (now: number) => { raf = 0; if (!visible || !sized || phase !== "grow") return; if (last === 0) last = now; acc += Math.min(100, now - last); last = now; while (acc >= STEP_MS) { acc -= STEP_MS; const grew = tick(); tickCount += 1; if (!grew) { stagnant += 1; } else { stagnant = 0; } if (stagnant >= STAGNANT_LIMIT || tickCount >= MAX_TICKS) { finishGrowth(); return; } } render(); raf = requestAnimationFrame(loop); }; startCycle(); // -- resize / layout observers: re-measure content boxes and restart // the whole cycle, so a moved headline genuinely changes the topology // rather than just clipping the same network differently. ------------ let resizeTimer = 0; const onResize = () => { window.clearTimeout(resizeTimer); resizeTimer = window.setTimeout(() => { if (disposed) return; cancelAnimationFrame(raf); raf = 0; window.clearTimeout(restTimer); window.clearTimeout(drainTimer); setDraining(false); clearPaths(); startCycle(); }, 120); }; const ro = new ResizeObserver(onResize); ro.observe(root); const io = new IntersectionObserver((entries) => { visible = entries[0]?.isIntersecting ?? true; if (visible && phase === "grow" && !raf) { last = 0; raf = requestAnimationFrame(loop); } }); io.observe(root); document.fonts.ready.then(() => { if (!disposed) onResize(); }); return () => { disposed = true; cancelAnimationFrame(raf); raf = 0; window.clearTimeout(restTimer); window.clearTimeout(drainTimer); window.clearTimeout(resizeTimer); ro.disconnect(); io.disconnect(); }; // eslint-disable-next-line react-hooks/exhaustive-deps }, [linesKey, sourceCount]); return (

{eyebrow}

{headlineLines.map((line, i) => ( {line} ))}

{subcopy}

{primaryCta.label} {secondaryCta.label}

{stats.slice(0, 3).map((s) => (

{s.value} {s.label.toUpperCase()}

))}

); } 27:oc3,68:["$","$L69",null,{"files":[{"path":"registry/core/auxin-canal/component.tsx","content":"$6a","type":"registry:ui","target":"components/ui/auxin-canal.tsx"}],"className":"h-[70svh] min-h-80"}] 27:o30,21:C 1f:C 20:C 16:C 1c:C 1d:C 23:false 22:48922 27:C