first commit. The hands pulse back and forth.

script.js

@@ -0,0 +1,87 @@
+let steps = 3;
+
+console.clear();
+
+const rules = {
+  "A": "+BF-AFA-FB+",
+  "B": "-AF+BFB+FA-",
+};
+
+let s = "A";
+for(let i=0;i<steps;i++) {
+  let ns = "";
+  for(let c of s) {
+    ns += rules[c] || c;
+  }
+  s = ns;
+}
+
+let [x,y] = [0,0];
+const m = 1/(2**steps-1);
+let dir = [m,0];
+let d = 'M 0 0 ';
+const width = 1.5 * 2**-(steps+1);
+
+const dots = [];
+
+for(let c of s) {
+  const [dx,dy] = dir;
+  switch(c) {
+    case '+':
+      dir = [-dy,dx];
+      break;
+    case '-':
+      dir = [dy,-dx];
+      break;
+    case 'F':
+      x += dx;
+      y += dy;
+      d += `l ${dx} ${dy}`;
+  }
+}
+
+d += 'l 0.000000001 0.000001'; // make sure the final dot is drawn
+
+const length = (2**(2*steps)-1) * m;
+
+const curves = Array.from(document.querySelectorAll('.curve'));
+
+for(let curve of curves) {
+  curve.setAttribute('stroke-width',width);
+  curve.setAttribute('stroke-linecap','round');
+  curve.setAttribute('stroke-dasharray',`${length} ${length}`);
+  curve.setAttribute('d',d);
+}
+document.getElementById('dots').setAttribute('stroke-width',width*0.4);
+document.getElementById('dots').setAttribute('d',d);
+document.getElementById('dots').setAttribute('stroke-dasharray',`0 ${m}`);
+
+function easeInOutSine(x) {
+  return -(Math.cos(Math.PI * x) - 1) / 2;
+}
+
+function easeLinear(t) {
+  return 1-2*Math.abs(t % 1 - 0.5);
+}
+
+function frame() {
+  const period = 1000;
+  const pips = 2**(2*steps)-1;
+  let scale = 1;
+  curves.forEach((curve,i) => {
+    const dt = (new Date() - 0) / scale / period;
+    const m = dt % (pips);
+    const t = dt;
+    const l = (Math.floor(m) + easeInOutSine(m % 1))*length/pips;
+    const n = Math.max(0,easeInOutSine(t))*l;
+    //document.getElementById('debug').textContent = `${m.toFixed(4)} ${length} ${pips}`
+    curve.setAttribute('stroke-dasharray',`${l-n} ${length}`);
+    curve.setAttribute('stroke-dashoffset',-n);
+    curve.setAttribute('stroke-width',width*(easeInOutSine(t)*0.1+0.9)/2**(i+1));
+
+    scale *= pips;
+  })
+  
+  requestAnimationFrame(frame);
+}
+frame();