diff --git a/app/demo/index.html b/app/demo/index.html
index 1638964..f3da360 100644
--- a/app/demo/index.html
+++ b/app/demo/index.html
@@ -91,33 +91,30 @@
   }
   .segmented {
     grid-column: 2 / -1;
-    display: grid;
-    grid-template-columns: repeat(6, 1fr);
-    border: 1px solid var(--hair);
-    background: var(--panel);
+    display: flex;
+    justify-content: space-between;
+    align-items: center;
   }
   .segmented label {
     font-family: "JetBrains Mono", "SF Mono", Menlo, Monaco, monospace;
     font-size: 12px;
-    text-align: center;
-    padding: 7px 0;
-    cursor: pointer;
     color: var(--muted);
-    border-left: 1px solid var(--hair);
-    transition: background 120ms ease, color 120ms ease;
+    cursor: pointer;
+    padding: 4px 2px 5px;
+    border-bottom: 1px solid transparent;
+    transition: color 120ms ease, border-color 120ms ease;
     user-select: none;
     font-variant-numeric: tabular-nums;
     position: relative;
   }
-  .segmented label:first-of-type { border-left: none; }
-  .segmented label:hover { color: var(--text); background: rgba(31, 78, 95, 0.06); }
+  .segmented label:hover { color: var(--text); }
   .segmented label:has(input:checked) {
-    background: var(--accent);
-    color: #fff;
+    color: var(--accent);
+    border-bottom-color: var(--accent);
   }
   .segmented label:has(input:focus-visible) {
-    outline: 2px solid var(--accent);
-    outline-offset: -2px;
+    outline: 1px solid var(--accent);
+    outline-offset: 2px;
   }
   .segmented input[type="radio"] {
     position: absolute;
@@ -347,6 +344,13 @@
     <label><input type="radio" name="j" value="0.15"><span>0.15</span></label>
     <label><input type="radio" name="j" value="0.2"><span>0.20</span></label>
   </div>
+
+  <span class="ctl-label">n frames</span>
+  <div class="segmented" role="radiogroup" aria-label="number of frames">
+    <label><input type="radio" name="f" value="12"><span>12</span></label>
+    <label><input type="radio" name="f" value="24" checked><span>24</span></label>
+    <label><input type="radio" name="f" value="48"><span>48</span></label>
+  </div>
 </div>
 
 <div class="gallery" id="gallery">
@@ -373,6 +377,11 @@
 import * as THREE from 'three';
 import { OrbitControls } from 'three/addons/controls/OrbitControls.js';
 
+// Trajectories are precomputed at the max cycle length. Toggling n-frames
+// truncates (12 is a prefix of 24 is a prefix of 48) so the same walk is
+// reused — no reroll on toggle, and the per-frame pulse stays consistent.
+const MAX_FRAMES = 48;
+
 const CATEGORICAL_HEX = [
   '#1f4e5f', '#c97b3f', '#8b5a9f', '#5a8560',
   '#c74a5e', '#6b7d8f', '#b89f51', '#4a6fa5',
@@ -412,18 +421,6 @@ function normalize(points) {
   return { positions: out, scaleFactor: 1 / maxAbs };
 }
 
-// Box-Muller: fills an array with standard-normal samples.
-function fillRandn(arr) {
-  for (let i = 0; i < arr.length; i += 2) {
-    const u1 = Math.random() || 1e-12;
-    const u2 = Math.random();
-    const mag = Math.sqrt(-2.0 * Math.log(u1));
-    arr[i] = mag * Math.cos(2 * Math.PI * u2);
-    if (i + 1 < arr.length) arr[i + 1] = mag * Math.sin(2 * Math.PI * u2);
-  }
-  return arr;
-}
-function randnArray(n) { return fillRandn(new Float32Array(n)); }
 
 function buildColors(labels, kind) {
   const n = labels.length;
@@ -485,20 +482,42 @@ function createScene(container, dataset) {
   controls.minDistance = 1.5;
   controls.maxDistance = 6;
 
-  const noiseLen = basePositions.length;
-  const SNAPSHOT_MS = 900;
   return {
     scene, camera, renderer, controls, container, geometry,
     basePositions,
     scaleFactor,
-    noiseA: randnArray(noiseLen),
-    noiseB: randnArray(noiseLen),
-    // random phase so the three scenes don't click over in lockstep
-    interpStartMs: performance.now() - Math.random() * SNAPSHOT_MS,
-    snapshotMs: SNAPSHOT_MS,
+    // trajectory state is populated by buildTrajectories() once at init
+    trajectories: null,
+    numFrames: 0,
+    snapshotMs: 1000 / 12,
+    // random phase so the three scenes don't loop in lockstep
+    cycleStartMs: performance.now() - Math.random() * 2000,
   };
 }
 
+// Build a cumulative random-walk trajectory for one scene.
+// Frame 0 is rest; each subsequent frame adds an independent unit-σ kick.
+// The render loop wraps frame N-1 → 0, giving a seamless cycle that ends
+// by pulling points back to base (mirrors an N-snapshot simulation's shape).
+function buildTrajectories(s, numFrames) {
+  const n = s.basePositions.length;
+  const buf = new Float32Array(numFrames * n);
+  for (let f = 1; f < numFrames; f++) {
+    const prev = (f - 1) * n;
+    const cur = f * n;
+    for (let j = 0; j < n; j += 2) {
+      const u1 = Math.random() || 1e-12;
+      const u2 = Math.random();
+      const mag = Math.sqrt(-2.0 * Math.log(u1));
+      buf[cur + j] = buf[prev + j] + mag * Math.cos(2 * Math.PI * u2);
+      if (j + 1 < n) buf[cur + j + 1] = buf[prev + j + 1] + mag * Math.sin(2 * Math.PI * u2);
+    }
+  }
+  s.trajectories = buf;
+  s.numFrames = numFrames;
+  s.cycleStartMs = performance.now() - Math.random() * s.snapshotMs * numFrames;
+}
+
 function sizeScene(s) {
   const rect = s.container.getBoundingClientRect();
   const size = Math.max(1, Math.floor(rect.width));
@@ -548,6 +567,8 @@ async function main() {
     const viz = card.querySelector('.viz');
     const s = createScene(viz, ds);
     sizeScene(s);
+    // Precompute at the max frame count; toggling only changes cycle length.
+    buildTrajectories(s, MAX_FRAMES);
     scenes.push(s);
 
     // Stop auto-rotate once the user interacts.
@@ -602,6 +623,24 @@ async function main() {
   const jChecked = document.querySelector('input[name="j"]:checked');
   applyJ(parseFloat(jChecked.value));
 
+  // n frames: truncates the precomputed walk. Prefix-stable (12 ⊂ 24 ⊂ 48),
+  // so toggling changes cycle length without rerolling. cycleStartMs is
+  // restaggered so the three cards don't sync up after a toggle.
+  let numFrames = 24;
+  const fInputs = document.querySelectorAll('input[name="f"]');
+  function applyF(n) {
+    numFrames = n;
+    for (const s of scenes) {
+      s.numFrames = n;
+      s.cycleStartMs = performance.now() - Math.random() * s.snapshotMs * n;
+    }
+  }
+  fInputs.forEach(input => {
+    input.addEventListener('change', (e) => applyF(parseInt(e.target.value, 10)));
+  });
+  const fChecked = document.querySelector('input[name="f"]:checked');
+  applyF(parseInt(fChecked.value, 10));
+
   // Keyboard: digits jump directly, arrows step.
   function selectByIndex(idx, { scroll = true } = {}) {
     const entry = order[idx];
@@ -643,32 +682,37 @@ async function main() {
     resizeTimer = setTimeout(() => scenes.forEach(sizeScene), 80);
   });
 
-  // Render loop.
+  // Render loop. Each scene walks through its cumulative trajectory,
+  // interpolating between consecutive frames; wraps from frame N-1 back to 0
+  // (which is rest, so the cycle naturally pulls points home).
   function tick() {
     requestAnimationFrame(tick);
     const now = performance.now();
     for (const s of scenes) {
-      // Advance the A→B snapshot transition; regenerate B when we roll over.
-      let t = (now - s.interpStartMs) / s.snapshotMs;
-      if (t >= 1) {
-        const tmp = s.noiseA; s.noiseA = s.noiseB; s.noiseB = tmp;
-        fillRandn(s.noiseB);
-        s.interpStartMs = now;
-        t = 0;
-      }
-      const total = s.basePositions.length / 3;
+      const N = s.numFrames;
+      const n = s.basePositions.length;
+      const cycleMs = N * s.snapshotMs;
+      const elapsed = ((now - s.cycleStartMs) % cycleMs + cycleMs) % cycleMs;
+      const frameF = elapsed / s.snapshotMs;
+      const frameIdx = Math.floor(frameF);
+      const interpT = frameF - frameIdx;
+      const nextIdx = (frameIdx + 1) % N;
+      const aOff = frameIdx * n;
+      const bOff = nextIdx * n;
+
+      const total = n / 3;
       const drawCount = s.geometry.drawRange.count;
       const visibleN = Number.isFinite(drawCount) ? Math.min(drawCount, total) : total;
       const limit = visibleN * 3;
       const pos = s.geometry.attributes.position.array;
       const base = s.basePositions;
-      const a = s.noiseA, b = s.noiseB;
+      const tr = s.trajectories;
       // Jitter is applied in normalized space so σ means the same thing
       // across datasets — independent of the raw feature magnitudes.
       const scale = jitterScale;
-      const u = 1 - t;
+      const u = 1 - interpT;
       for (let i = 0; i < limit; i++) {
-        pos[i] = base[i] + (a[i] * u + b[i] * t) * scale;
+        pos[i] = base[i] + (tr[aOff + i] * u + tr[bOff + i] * interpT) * scale;
       }
       s.geometry.attributes.position.needsUpdate = true;