04シェルピンスキーの三角形 — 三角形に潜む三角形

<main class="stage">
<div class="ls is-demo" id="lsRoot">
  <p class="ls__hint">
    <span>A→B-A-B、B→A+B+A の2文字を60°の亀歩きで展開すると一筆書きの矢じり曲線になります。世代を重ねるほど、その曲線がシェルピンスキーの三角形の隙間をそのまま埋めていきます</span>
  </p>
  <div class="ls__field" role="application" aria-label="シェルピンスキーの三角形ラボ" tabindex="0">
    <canvas class="ls__cv" id="lsCv"></canvas>
  </div>
  <div class="ls__bar">
    <span class="ls__meta">規則 A→B-A-B · 角度60° · 世代 <b id="lsGen">0</b></span>
    <span class="ls__meta ls__meta--dim">canvas · 文字列書き換え · beginPath</span>
  </div>
</div>
</main>

@use "../../../../site/static/demo-tokens" as *;

// 셸핀스키 삼각형(04). @keyframes 를 두지 않는다 —
// 움직임은 전부 캔버스 rAF 루프(화살촉 곡선 세대 크로스페이드 + 도는 빛)가 만든다.
// 무대는 편 공통 숲 밤 이끼(01~03 과 동일 팔레트).

$duration: $dur-loop;
$easing: $ease-spring;
$color: $subject-mint;

$ls-stage: #1a2116;
@include stage($ls-stage);

$ls-ink:   #12160e;
$ls-bark2: #e6d8bc;
$ls-leaf:  #bfe3c8;
$ls-mist:  #dfe6d6;

.ls {
  --ls-ink:   #{$ls-ink};
  --ls-bark2: #{$ls-bark2};
  --ls-leaf:  #{$ls-leaf};
  --ls-mist:  #{$ls-mist};

  display: flex; flex-direction: column; gap: $sp-2;
  width: 100%; max-width: 424px;
}

.ls__hint {
  display: flex; align-items: center; gap: $sp-1; margin: 0;
  font-weight: 700; font-size: clamp(10px, 2.8vw, 12px); line-height: 1.35;
  color: $ls-mist;
}

.ls__field {
  position: relative; height: 180px;
  border-radius: $r-card; overflow: hidden;
  background: $ls-ink;
  box-shadow: inset 0 0 0 1px rgba($ls-mist, .18);
}
.ls__field:focus-visible { outline: 2px solid $subject-mint; outline-offset: 2px; }

.ls__cv { display: block; width: 100%; height: 100%; }

.ls__bar { display: flex; align-items: baseline; justify-content: space-between; gap: $sp-2; }
.ls__meta { font-size: 10px; font-weight: 500; color: rgba($ls-mist, .72); }
.ls__meta--dim { font-size: 10px; }
.ls__meta b { font-weight: 700; color: $ls-mist; }

@media (max-width: 340px) {
  .ls { gap: $sp-1; }
  .ls__field { height: 100px; }
  .ls__meta--dim { display: none; }
}

@media (prefers-reduced-motion: reduce) {
  .ls.is-still .ls__field { cursor: default !important; }
}

html, body {
  margin: 0;
  overflow: hidden;
}

.stage {
  box-sizing: border-box;
  min-height: 100vh;
  display: grid;
  place-items: center;
  margin: 0;
  background: #1a2116;
  font-family: -apple-system, "Segoe UI", "Noto Sans KR", sans-serif;
  padding: clamp(8px, 4vw, 24px);
}

.ls {
  --ls-ink: #12160e;
  --ls-bark2: #e6d8bc;
  --ls-leaf: #bfe3c8;
  --ls-mist: #dfe6d6;
  display: flex;
  flex-direction: column;
  gap: 8px;
  width: 100%;
  max-width: 424px;
}

.ls__hint {
  display: flex;
  align-items: center;
  gap: 4px;
  margin: 0;
  font-weight: 700;
  font-size: clamp(10px, 2.8vw, 12px);
  line-height: 1.35;
  color: #dfe6d6;
}

.ls__field {
  position: relative;
  height: 180px;
  border-radius: 16px;
  overflow: hidden;
  background: #12160e;
  box-shadow: inset 0 0 0 1px rgba(223, 230, 214, 0.18);
}

.ls__field:focus-visible {
  outline: 2px solid #4cd4a6;
  outline-offset: 2px;
}

.ls__cv {
  display: block;
  width: 100%;
  height: 100%;
}

.ls__bar {
  display: flex;
  align-items: baseline;
  justify-content: space-between;
  gap: 8px;
}

.ls__meta {
  font-size: 10px;
  font-weight: 500;
  color: rgba(223, 230, 214, 0.72);
}

.ls__meta--dim {
  font-size: 10px;
}

.ls__meta b {
  font-weight: 700;
  color: #dfe6d6;
}

@media (max-width: 340px) {
  .ls {
    gap: 4px;
  }
  .ls__field {
    height: 100px;
  }
  .ls__meta--dim {
    display: none;
  }
}
@media (prefers-reduced-motion: reduce) {
  .ls.is-still .ls__field {
    cursor: default !important;
  }
}

// 셸핀스키 삼각형(04) — 화살촉(Arrowhead) L-시스템: A,B 두 기호가 서로를 끼워 넣으며
// 자라는 한붓그리기 곡선이 세대가 늘수록 삼각형 가스켓의 구멍을 정확히 남긴다.
// 움직임 = 世代 크로스페이드 성장(0→6) + 완성 뒤 곡선을 따라 도는 빛 한 점.
(function () {
  // ── 변형 상수 블록 ──
  var ANGLE  = 60;
  var MAXGEN = 6;
  var CYCLE  = 2.0;
  // ─────────────────

  var root = document.getElementById('lsRoot');
  var field = document.getElementById('lsCv').parentElement;
  var cv = document.getElementById('lsCv');
  var genEl = document.getElementById('lsGen');

  var css = getComputedStyle(root);
  function tokRGB(name) {
    var s = css.getPropertyValue(name).trim();
    var hx = s.length === 4
      ? s.charAt(1) + s.charAt(1) + s.charAt(2) + s.charAt(2) + s.charAt(3) + s.charAt(3)
      : s.slice(1);
    return [parseInt(hx.slice(0, 2), 16), parseInt(hx.slice(2, 4), 16), parseInt(hx.slice(4, 6), 16)];
  }
  var C_LINE = tokRGB('--ls-bark2');
  var C_GLOW = tokRGB('--ls-leaf');
  var C_INK  = tokRGB('--ls-ink');

  var reduce = window.matchMedia('(prefers-reduced-motion: reduce)').matches;
  var raf = 0, t0 = -1;
  var W = 0, H = 0;

  function fit() {
    var r = field.getBoundingClientRect();
    W = Math.round(r.width); H = Math.round(r.height);
    cv.width = W; cv.height = H;
  }

  var RULE = { 'A': 'B-A-B', 'B': 'A+B+A' };
  function expand(axiom, gen) {
    var s = axiom;
    for (var g = 0; g < gen; g++) {
      var out = '';
      for (var i = 0; i < s.length; i++) {
        var ch = s.charAt(i);
        out += RULE[ch] !== undefined ? RULE[ch] : ch;
      }
      s = out;
    }
    return s;
  }

  // 거북 해석 — A,B 모두 전진 한 걸음, +,- 는 60도 회전. 열린 곡선 점 목록을 만든다.
  function turtlePath(str, step) {
    var x = 0, y = 0, a = 0;
    var pts = [{ x: x, y: y }];
    for (var i = 0; i < str.length; i++) {
      var ch = str.charAt(i);
      if (ch === 'A' || ch === 'B') {
        x += Math.cos(a) * step;
        y += Math.sin(a) * step;
        pts.push({ x: x, y: y });
      } else if (ch === '+') {
        a -= ANGLE * Math.PI / 180;
      } else if (ch === '-') {
        a += ANGLE * Math.PI / 180;
      }
    }
    return pts;
  }

  var AXIOM = 'A';
  var POLY = [];
  (function precompute() {
    var strs = [];
    for (var g = 0; g <= MAXGEN; g++) strs.push(expand(AXIOM, g));
    var raw = [];
    for (var g2 = 0; g2 <= MAXGEN; g2++) raw.push(turtlePath(strs[g2], 1 / Math.pow(2, g2)));
    var last = raw[MAXGEN];
    var minX = Infinity, maxX = -Infinity, minY = Infinity, maxY = -Infinity;
    for (var i = 0; i < last.length; i++) {
      minX = Math.min(minX, last[i].x); maxX = Math.max(maxX, last[i].x);
      minY = Math.min(minY, last[i].y); maxY = Math.max(maxY, last[i].y);
    }
    var span = Math.max(maxX - minX, maxY - minY) || 1;
    for (var g3 = 0; g3 <= MAXGEN; g3++) {
      var norm = [];
      for (var j = 0; j < raw[g3].length; j++) {
        norm.push({ x: (raw[g3][j].x - minX) / span, y: (raw[g3][j].y - minY) / span });
      }
      POLY.push(norm);
    }
  })();

  function rgb(c, a) {
    return 'rgba(' + (c[0] | 0) + ',' + (c[1] | 0) + ',' + (c[2] | 0) + ',' + a + ')';
  }

  function drawPath(ctx, pts, ox, oy, sc, col, alpha, lw) {
    if (!pts.length) return;
    ctx.strokeStyle = rgb(col, alpha);
    ctx.lineWidth = lw;
    ctx.beginPath();
    ctx.moveTo(ox + pts[0].x * sc, oy + pts[0].y * sc);
    for (var i = 1; i < pts.length; i++) ctx.lineTo(ox + pts[i].x * sc, oy + pts[i].y * sc);
    ctx.stroke();
  }

  function render(loop) {
    var ctx = cv.getContext('2d');
    ctx.fillStyle = rgb(C_INK, 1);
    ctx.fillRect(0, 0, W, H);

    var sc = Math.min(W, H) * 0.82;
    var ox = (W - sc) / 2, oy = (H - sc) / 2;

    var grPhase = Math.min(loop / 0.68, 1);
    var genF = grPhase * MAXGEN;
    var gA = Math.min(MAXGEN, Math.floor(genF));
    var gB = Math.min(MAXGEN, gA + 1);
    var f = genF - gA;

    // 세대가 늘수록 선분 간격이 좁아지므로 굵기를 간격에 맞춰 키운다 —
    // 화살촉 곡선이 스스로 겹치며 가스켓 안쪽을 실제로 채운다(피사체를 키운다 원칙)
    var lwA = Math.min(4.2, Math.max(1.3, sc / Math.pow(2, gA) * 0.62));
    var lwB = Math.min(4.2, Math.max(1.1, sc / Math.pow(2, gB) * 0.62));
    drawPath(ctx, POLY[gA], ox, oy, sc, C_LINE, 1, lwA);
    if (f > 0 && gB !== gA) drawPath(ctx, POLY[gB], ox, oy, sc, C_GLOW, f, lwB);

    if (genEl) genEl.textContent = String(gA);

    if (loop >= 0.68) {
      var t = (loop - 0.68) / 0.32;
      var pts = POLY[MAXGEN];
      var idxF = t * (pts.length - 1);
      var i0 = Math.floor(idxF) % (pts.length - 1);
      var lf = idxF - Math.floor(idxF);
      var p0 = pts[i0], p1 = pts[i0 + 1] || pts[pts.length - 1];
      var lx = ox + (p0.x + (p1.x - p0.x) * lf) * sc;
      var ly = oy + (p0.y + (p1.y - p0.y) * lf) * sc;
      ctx.fillStyle = rgb(C_GLOW, 0.9);
      ctx.beginPath();
      ctx.arc(lx, ly, 3, 0, Math.PI * 2);
      ctx.fill();
    }
  }

  function frame(now) {
    if (t0 < 0) t0 = now;
    var loop = (((now - t0) / 1000) % CYCLE) / CYCLE;
    render(loop);
    raf = requestAnimationFrame(frame);
  }

  window.addEventListener('resize', function () {
    fit();
    render(reduce ? 0.85 : 0.8);
  });

  fit();
  if (reduce) {
    render(0.85);
    root.classList.add('is-still');
  } else {
    raf = requestAnimationFrame(frame);
  }
})();

// LsysSierpinskiTriangle — vanilla 판(run/328/demo/04-lsys-sierpinski-triangle/index.html) 의 React 포트.
// 화살촉(Arrowhead) L-시스템: A,B 두 기호가 서로를 끼워 넣으며 자라는 한붓그리기 곡선이
// 세대가 늘수록 삼각형 가스켓의 구멍을 정확히 남긴다.
// 움직임 = 세대 크로스페이드 성장(0→6) + 완성 뒤 곡선을 따라 도는 빛 한 점.
import { useEffect, useRef, useState } from "react";
import type { CSSProperties } from "react";
import styles from "./LsysSierpinskiTriangle.module.scss";

export type LsysSierpinskiTriangleProps = {
  duration?: string;
  easing?: string;
  color?: string;
  angle?: number;
  maxGen?: number;
  cycle?: number;
};

const ANGLE = 60;
const MAXGEN = 6;
const CYCLE = 2.0;

type Vars = CSSProperties & { "--duration"?: string; "--easing"?: string; "--color"?: string };
type Box<T> = { current: T };
type RGB = [number, number, number];
type XY = { x: number; y: number };

const HINT_TEXT = "A→B-A-B, B→A+B+A 두 문자를 60° 거북 걸음으로 풀면 한붓그리기 화살촉 곡선이 되는데, 세대를 더할수록 그 곡선이 셸핀스키 삼각형의 빈틈을 그대로 메웁니다";
const META_LEFT_PREFIX = "규칙 A→B-A-B · 각도 60° · 세대 ";
const META_RIGHT = "canvas · 문자 재쓰기 · beginPath";
const FIELD_LABEL = "셸핀스키 삼각형 실험판";

const RULE: Record<string, string> = { A: "B-A-B", B: "A+B+A" };
function expand(axiom: string, gen: number): string {
  let s = axiom;
  for (let g = 0; g < gen; g++) {
    let out = "";
    for (let i = 0; i < s.length; i++) {
      const ch = s.charAt(i);
      out += RULE[ch] !== undefined ? RULE[ch] : ch;
    }
    s = out;
  }
  return s;
}

function turtlePath(str: string, step: number, angle: number): XY[] {
  let x = 0, y = 0, a = 0;
  const pts: XY[] = [{ x, y }];
  for (let i = 0; i < str.length; i++) {
    const ch = str.charAt(i);
    if (ch === "A" || ch === "B") {
      x += Math.cos(a) * step;
      y += Math.sin(a) * step;
      pts.push({ x, y });
    } else if (ch === "+") {
      a -= angle * Math.PI / 180;
    } else if (ch === "-") {
      a += angle * Math.PI / 180;
    }
  }
  return pts;
}

const AXIOM = "A";
function buildPoly(angle: number, maxGen: number): XY[][] {
  const strs: string[] = [];
  for (let g = 0; g <= maxGen; g++) strs.push(expand(AXIOM, g));
  const raw: XY[][] = [];
  for (let g2 = 0; g2 <= maxGen; g2++) raw.push(turtlePath(strs[g2], 1 / Math.pow(2, g2), angle));
  const last = raw[maxGen];
  let minX = Infinity, maxX = -Infinity, minY = Infinity, maxY = -Infinity;
  for (let i = 0; i < last.length; i++) {
    minX = Math.min(minX, last[i].x); maxX = Math.max(maxX, last[i].x);
    minY = Math.min(minY, last[i].y); maxY = Math.max(maxY, last[i].y);
  }
  const span = Math.max(maxX - minX, maxY - minY) || 1;
  const poly: XY[][] = [];
  for (let g3 = 0; g3 <= maxGen; g3++) {
    const norm: XY[] = [];
    for (let j = 0; j < raw[g3].length; j++) {
      norm.push({ x: (raw[g3][j].x - minX) / span, y: (raw[g3][j].y - minY) / span });
    }
    poly.push(norm);
  }
  return poly;
}

function rgba(c: RGB, a: number): string {
  return "rgba(" + (c[0] | 0) + "," + (c[1] | 0) + "," + (c[2] | 0) + "," + a + ")";
}

export default function LsysSierpinskiTriangle({
  duration = "2s",
  easing = "ease-spring",
  color = "#bfe3c8",
  angle = ANGLE,
  maxGen = MAXGEN,
  cycle = CYCLE
}: LsysSierpinskiTriangleProps) {
  const rootRef = useRef<HTMLDivElement | null>(null);
  const fieldRef = useRef<HTMLDivElement | null>(null);
  const cvRef = useRef<HTMLCanvasElement | null>(null);
  const ctxRef = useRef<CanvasRenderingContext2D | null>(null);
  const colRef = useRef<{ line: RGB; glow: RGB; ink: RGB } | null>(null);
  const polyRef = useRef<XY[][]>([]) as Box<XY[][]>;
  const wRef = useRef(0) as Box<number>;
  const hRef = useRef(0) as Box<number>;
  const rafRef = useRef(0) as Box<number>;
  const [still, setStill] = useState(false);
  const [gen, setGen] = useState(0);
  const vars: Vars = { "--duration": duration, "--easing": easing, "--color": color };

  function reduced(): boolean {
    return window.matchMedia("(prefers-reduced-motion: reduce)").matches;
  }

  function tokRGB(root: HTMLDivElement, name: string): RGB {
    const s = getComputedStyle(root).getPropertyValue(name).trim();
    const hx = s.length === 4
      ? s.charAt(1) + s.charAt(1) + s.charAt(2) + s.charAt(2) + s.charAt(3) + s.charAt(3)
      : s.slice(1);
    return [parseInt(hx.slice(0, 2), 16), parseInt(hx.slice(2, 4), 16), parseInt(hx.slice(4, 6), 16)];
  }

  function fit(): void {
    const field = fieldRef.current;
    const cv = cvRef.current;
    if (!field || !cv) return;
    const r = field.getBoundingClientRect();
    wRef.current = Math.round(r.width);
    hRef.current = Math.round(r.height);
    cv.width = wRef.current;
    cv.height = hRef.current;
  }

  function drawPath(ctx: CanvasRenderingContext2D, pts: XY[], ox: number, oy: number, sc: number, col: RGB, alpha: number, lw: number): void {
    if (!pts.length) return;
    ctx.strokeStyle = rgba(col, alpha);
    ctx.lineWidth = lw;
    ctx.beginPath();
    ctx.moveTo(ox + pts[0].x * sc, oy + pts[0].y * sc);
    for (let i = 1; i < pts.length; i++) ctx.lineTo(ox + pts[i].x * sc, oy + pts[i].y * sc);
    ctx.stroke();
  }

  function draw(loop: number): void {
    const ctx = ctxRef.current;
    const col = colRef.current;
    const POLY = polyRef.current;
    const W = wRef.current, H = hRef.current;
    if (!ctx || !col || !POLY.length) return;
    ctx.fillStyle = rgba(col.ink, 1);
    ctx.fillRect(0, 0, W, H);

    const sc = Math.min(W, H) * 0.82;
    const ox = (W - sc) / 2, oy = (H - sc) / 2;

    const grPhase = Math.min(loop / 0.68, 1);
    const genF = grPhase * maxGen;
    const gA = Math.min(maxGen, Math.floor(genF));
    const gB = Math.min(maxGen, gA + 1);
    const f = genF - gA;

    const lwA = Math.min(4.2, Math.max(1.3, sc / Math.pow(2, gA) * 0.62));
    const lwB = Math.min(4.2, Math.max(1.1, sc / Math.pow(2, gB) * 0.62));
    drawPath(ctx, POLY[gA], ox, oy, sc, col.line, 1, lwA);
    if (f > 0 && gB !== gA) drawPath(ctx, POLY[gB], ox, oy, sc, col.glow, f, lwB);

    setGen(gA);

    if (loop >= 0.68) {
      const t = (loop - 0.68) / 0.32;
      const pts = POLY[maxGen];
      const idxF = t * (pts.length - 1);
      const i0 = Math.floor(idxF) % (pts.length - 1);
      const lf = idxF - Math.floor(idxF);
      const p0 = pts[i0], p1 = pts[i0 + 1] || pts[pts.length - 1];
      const lx = ox + (p0.x + (p1.x - p0.x) * lf) * sc;
      const ly = oy + (p0.y + (p1.y - p0.y) * lf) * sc;
      ctx.fillStyle = rgba(col.glow, 0.9);
      ctx.beginPath();
      ctx.arc(lx, ly, 3, 0, Math.PI * 2);
      ctx.fill();
    }
  }

  let t0 = -1;
  function frame(now: number): void {
    if (t0 < 0) t0 = now;
    const loop = (((now - t0) / 1000) % cycle) / cycle;
    draw(loop);
    rafRef.current = requestAnimationFrame(frame);
  }

  useEffect(() => {
    const root = rootRef.current;
    const cv = cvRef.current;
    if (!root || !cv) return;
    colRef.current = {
      line: tokRGB(root, "--ls-bark2"),
      glow: tokRGB(root, "--ls-leaf"),
      ink: tokRGB(root, "--ls-ink")
    };
    polyRef.current = buildPoly(angle, maxGen);
    ctxRef.current = cv.getContext("2d");
    fit();
    const reduce = reduced();
    function onResize(): void {
      fit();
      draw(0.8);
    }
    window.addEventListener("resize", onResize);
    if (reduce) {
      draw(0.85);
      setStill(true);
    } else {
      t0 = -1;
      rafRef.current = requestAnimationFrame(frame);
    }
    return () => {
      window.removeEventListener("resize", onResize);
      cancelAnimationFrame(rafRef.current);
    };
    // eslint-disable-next-line react-hooks/exhaustive-deps
  }, [angle, maxGen, cycle]);

  const rootCls = still ? `${styles.root} ${styles.isStill}` : styles.root;

  return (
    <main className={styles.stage}>
      <div className={rootCls} ref={rootRef} style={vars}>
        <p className={styles.hint}><span>{HINT_TEXT}</span></p>
        <div className={styles.field} ref={fieldRef} role="application" aria-label={FIELD_LABEL} tabIndex={0}>
          <canvas className={styles.cv} ref={cvRef}></canvas>
        </div>
        <div className={styles.bar}>
          <span className={styles.meta}>{META_LEFT_PREFIX}<b>{gen}</b></span>
          <span className={`${styles.meta} ${styles.metaDim}`}>{META_RIGHT}</span>
        </div>
      </div>
    </main>
  );
}