diff --git a/common.ts b/common.ts
index e6fdea3..7fd27cf 100644
--- a/common.ts
+++ b/common.ts
@@ -61,8 +61,8 @@ export function cubicBezier(a: Point, b: Point, c: Point, d: Point, res=0.05) {
 
 export function resizeCanvas(ctx: CanvasRenderingContext2D) {
     ctx.clearRect(0, 0, ctx.canvas.width, ctx.canvas.height);
-    ctx.canvas.width  = window.innerWidth;
-    ctx.canvas.height = window.innerHeight;
+    ctx.canvas.width = ctx.canvas.clientWidth;
+    ctx.canvas.height = ctx.canvas.clientHeight;
 }
 
 export function drawCircle(ctx: CanvasRenderingContext2D, center: Point, radius: number, color: number) {
diff --git a/move.ts b/move.ts
index ef5a478..acd966b 100644
--- a/move.ts
+++ b/move.ts
@@ -1,49 +1,80 @@
 import Vec2d from "./vec.js";
 import { drawCircle, resizeCanvas } from "./common.js";
 
+const SEGMENT_SPACING = 100;
+
+function initTrail(pos: Vec2d, len: number) {
+  return Array.from({ length: len }, (_, i) => pos.add(new Vec2d(0, -1).scale(i * SEGMENT_SPACING)));
+}
+
 // state
 let target: Vec2d | undefined = undefined;
-let pos = new Vec2d(200, 200);
+let trail = initTrail(new Vec2d(200, 200), 5);
 let velocity = new Vec2d(500, 500);
 let pause = false;
 let mode: "follow" | "bounce" = "bounce";
-let start: number | undefined = undefined;
+let lastFrameTime: number | undefined = undefined;
 
 function update(ctx: CanvasRenderingContext2D, timestamp: number) {
+  if (!lastFrameTime) lastFrameTime = timestamp;
+  const dt = (timestamp - lastFrameTime) / 1000; // seconds
+  lastFrameTime = timestamp;
     switch (mode) {
-        case "bounce":
-            updateBounce(ctx, timestamp);
-        break;
-        case "follow":
-            updateFollow(ctx);
-        break;
-        default:
-            throw new Error(`Unknown mode: ${mode}`);
+        case "bounce": updateBounce(ctx, dt); break;
+        case "follow": updateFollow(ctx, dt); break;
+        default: throw new Error(`Unknown mode: ${mode}`);
     }
     if (!pause) window.requestAnimationFrame(t => update(ctx, t));
 }
 
-function updateFollow(ctx: CanvasRenderingContext2D) {
-    if (target) pos = pos.lerp(target, 0.01);
-    ctx.clearRect(0, 0, ctx.canvas.width, ctx.canvas.height);
-    drawCircle(ctx, pos, 100, 0xFF00FF);
+function updateFollow(ctx: CanvasRenderingContext2D, dt: number) {
+  if (target) {
+    // update head position towards the mouse cursor
+    // using lerp with a factor of 0.1 moves 10% towards the target at each
+    // frame, so this is framerate dependent:
+    // trail[0] = trail[0].lerp(target, 0.1);
+    // use exponential decay instead, this is framerate independent:
+    const alpha = Math.exp(-10 * dt)
+    trail[0] = trail[0].lerp(target, alpha);
+    updateTrail();
+  }
+
+  ctx.clearRect(0, 0, ctx.canvas.width, ctx.canvas.height);
+  for (const pos of trail) {
+    drawCircle(ctx, pos, 20, 0xFF00FF);
+  }
 }
 
-function updateBounce(ctx: CanvasRenderingContext2D, timestamp: number) {
-    if (!start) start = timestamp;
-    const dt = timestamp - start;
+function updateBounce(ctx: CanvasRenderingContext2D, dt: number) {
+    // update head pos
     // P_t+1 = P_t + V * t
-    const newPos = pos.add(velocity.scale(0.001*dt));
+    const newPos = trail[0].add(velocity.scale(0.001*dt));
     if (newPos.x > ctx.canvas.width - 100) { velocity.x *= -1; newPos.x = ctx.canvas.width - 100; }
     if (newPos.y > ctx.canvas.height - 100) { velocity.y *= -1; newPos.y = ctx.canvas.height - 100; }
     if (newPos.x < 100) { velocity.x *= -1; newPos.x = 100; }
     if (newPos.y < 100) { velocity.y *= -1; newPos.y = 100; }
-    //console.log(velocity);
+    trail[0] = newPos;
+    updateTrail();
 
-    pos = newPos;
     ctx.clearRect(0, 0, ctx.canvas.width, ctx.canvas.height);
-    drawCircle(ctx, pos, 100, 0xFF00FF);
-    start = timestamp;
+    for (const pos of trail) {
+      drawCircle(ctx, pos, 20, 0xFF00FF);
+    }
+}
+
+function updateTrail() {
+  // "follow the leader" algorithm: keep segments at a fixed distance
+  // from each other by moving each segment towards the segment in front of it.
+  for (let i = 1; i < trail.length; i++) {
+    const leader = trail[i - 1];
+    const delta = leader.sub(trail[i]);
+    const dist = delta.length();
+    if (dist > SEGMENT_SPACING) {
+      const remainder = dist - SEGMENT_SPACING; // excess distance to be covered
+      const p = remainder / dist; // [0, 1]
+      trail[i] = trail[i].lerp(leader, p);
+    }
+  }
 }
 
 function init() {
@@ -51,10 +82,8 @@ function init() {
     if (!canvas) throw new Error("unable to get canvas HTML element");
     const ctx = canvas.getContext("2d") as CanvasRenderingContext2D | null;
     if (!ctx) throw new Error("unable to get canvas 2D context");
-
-    ctx.canvas.width  = window.innerWidth;
-    ctx.canvas.height = window.innerHeight;
-
+    ctx.canvas.width = ctx.canvas.clientWidth;
+    ctx.canvas.height = ctx.canvas.clientHeight;
 
     canvas.onmousemove = (evt) => {
         const {clientX, clientY} = evt;
@@ -69,10 +98,8 @@ function init() {
     }
 
     window.onkeydown = (evt) => {
-        console.log("key down", evt);
         if (mode === "follow") mode = "bounce";
         else mode = "follow"
-        console.log("mode", mode);
     }
 
     window.addEventListener('resize', () => resizeCanvas(ctx));
diff --git a/snake.ts b/snake.ts
index 0f55541..2d504cd 100644
--- a/snake.ts
+++ b/snake.ts
@@ -1,5 +1,5 @@
 import Vec2d from "./vec.js";
-import { fillCircle, lerp, lerpRgb } from "./common.js";
+import { resizeCanvas, fillCircle, lerp, lerpRgb } from "./common.js";
 
 // constants
 const SNAKE_RADIUS = 10;
@@ -27,12 +27,6 @@ let speed = 200; // px/s
 let interpolation_factor = 10;
 let paused = false;
 
-function resizeCanvas(ctx: CanvasRenderingContext2D) {
-  ctx.canvas.width = ctx.canvas.clientWidth;
-  ctx.canvas.height = ctx.canvas.clientHeight;
-  ctx.clearRect(0, 0, ctx.canvas.width, ctx.canvas.height);
-}
-
 let lastTime: number | undefined = undefined;
 
 function drawSnake(ctx: CanvasRenderingContext2D, bounds: Vec2d) {
diff --git a/vec.ts b/vec.ts
index 97f9345..042d7d7 100644
--- a/vec.ts
+++ b/vec.ts
@@ -21,6 +21,11 @@ export default class Vec2d implements Point {
     return `[${this.x}, ${this.y}]`;
   }
 
+  normalize(): Vec2d {
+    const len = this.length();
+    return new Vec2d(this.x / len, this.y / len);
+  }
+
   scale(scalar: number): Vec2d {
     return new Vec2d(this.x * scalar, this.y * scalar);
   }