diff --git a/README.md b/README.md
index d37b83e..557518b 100644
--- a/README.md
+++ b/README.md
@@ -33,7 +33,8 @@ Collect `6`, then `×`, then `4` → `6 × 4 = 24` ✓
 
 - Collect a number, an operator, a number… to build a running total.
 - Only your **latest** number and operator count — eat a better one to replace it.
-- Hitting a wall, biting your own tail, or letting the clock expire each costs a life.
+- Hitting a wall wraps the snake to the opposite side — no penalty.
+- Biting your own tail or letting the clock expire costs a life.
 - Three lives per run.
 
 ### Progression
diff --git a/public/css/style.css b/public/css/style.css
index 0cff6cb..362195d 100644
--- a/public/css/style.css
+++ b/public/css/style.css
@@ -148,7 +148,7 @@ body{
 .flash.good{background:radial-gradient(circle,rgba(120,220,150,.0),rgba(90,210,140,.35));animation:flash .5s ease;}
 @keyframes flash{0%{opacity:0}30%{opacity:1}100%{opacity:0}}
 
-.ent{position:absolute;left:0;top:0;width:var(--cell);height:var(--cell);display:flex;align-items:center;justify-content:center;transition:transform .075s linear;will-change:transform;}
+.ent{position:absolute;left:0;top:0;width:var(--cell);height:var(--cell);display:flex;align-items:center;justify-content:center;transition:transform .075s linear,opacity .075s linear;will-change:transform;}
 .ent.notrans{transition:none;}
 .box{width:84%;height:84%;display:flex;align-items:center;justify-content:center;font-family:'Fredoka';font-weight:600;font-size:calc(var(--cell)*.42);position:relative;}
 .box.num{background:var(--num-bg);color:var(--num-fg);border-radius:50%;box-shadow:0 3px 0 rgba(0,0,0,.14);}
diff --git a/public/js/main.js b/public/js/main.js
index 41cc07e..24e9361 100644
--- a/public/js/main.js
+++ b/public/js/main.js
@@ -152,6 +152,7 @@ function render() {
   renderRibbon({ tokens: ft, total: totalValue(), solved: isSolved(), pendingOp: curFrame().op, openGroups: G.frames.length > 1 });
   renderGrid(G, cell, ft);
   G.noTrans = false;
+  G.wrapGhost = null;
 }
 
 function schedule() { clearTimeout(tickTimer); if (G.running) tickTimer = setTimeout(step, G.tickMs); }
@@ -160,8 +161,14 @@ function step() {
   if (!G.running) return;
   G.dir = G.nextDir;
   const pos = nextHead(G.snake, G.dir, COLS, ROWS);
-  if (!pos) { crash(); schedule(); return; }
   if (collidesWithSelf(G.snake, pos)) { crash(); schedule(); return; }
+  const head = G.snake[0];
+  const isWrap = Math.abs(head.x - pos.x) > 1 || Math.abs(head.y - pos.y) > 1;
+  G.wrapGhost = isWrap ? {
+    entryFrom: { x: pos.x - G.dir.x, y: pos.y - G.dir.y }, // one cell outside entry wall
+    exitFrom:  { x: head.x, y: head.y },                    // old head position
+    exitTo:    { x: head.x + G.dir.x, y: head.y + G.dir.y }, // one cell past exit wall
+  } : null;
   const ti = G.tiles.findIndex(t => t.x === pos.x && t.y === pos.y);
   if (ti >= 0) { eatTile(ti, pos); schedule(); return; }
   G.snake = advance(G.snake, pos);
@@ -313,7 +320,7 @@ function startGame() {
     biome: 'garden', score: 0, lives: 3, target: 10, timeLeft: 26, timerMax: 26,
     frames: [{ tokens: [], acc: null, op: null }], history: [], snake: [],
     dir: { x: 1, y: 0 }, nextDir: { x: 1, y: 0 }, tiles: [],
-    tickMs: 160, baseTick: 160, running: false, solved: 0, longest: 0, noTrans: true
+    tickMs: 160, baseTick: 160, running: false, solved: 0, longest: 0, noTrans: true, wrapGhost: null
   };
   applyBiome('garden');
   app.dataset.screen = 'game';
diff --git a/public/js/snake.js b/public/js/snake.js
index 7ad1e50..cb4627e 100644
--- a/public/js/snake.js
+++ b/public/js/snake.js
@@ -5,11 +5,11 @@ export function createSnake(cols = COLS, rows = ROWS) {
   return [{ x: Math.floor(cols / 2), y: Math.floor(rows / 2) }];
 }
 
-// Returns the new head position, or null if it would leave the grid.
 export function nextHead(snake, dir, cols = COLS, rows = ROWS) {
-  const nx = snake[0].x + dir.x, ny = snake[0].y + dir.y;
-  if (nx < 0 || ny < 0 || nx >= cols || ny >= rows) return null;
-  return { x: nx, y: ny };
+  return {
+    x: (snake[0].x + dir.x + cols) % cols,
+    y: (snake[0].y + dir.y + rows) % rows,
+  };
 }
 
 // Checks all segments except the last tail cell (which will vacate on the same tick).
diff --git a/public/js/ui.js b/public/js/ui.js
index 510e841..0c511b9 100644
--- a/public/js/ui.js
+++ b/public/js/ui.js
@@ -78,18 +78,43 @@ export function renderGrid(G, cell, tokens) {
 
   // Body segments spell the running expression, most-recent token nearest the head.
   const bodyTokens = tokens.slice().reverse();
+  let headHTML = null;
   G.snake.forEach((p, i) => {
     const inner = i === 0
       ? `<div class="box head"><span class="eye l"></span><span class="eye r"></span></div>`
       : `<div class="box seg">${bodyTokens[i - 1] !== undefined ? bodyTokens[i - 1] : ''}</div>`;
-    ents.push({ k: 's' + i, x: p.x, y: p.y, html: inner });
+    if (i === 0) headHTML = inner;
+    const wrapFrom = (i === 0 && G.wrapGhost) ? G.wrapGhost.entryFrom : null;
+    ents.push({ k: 's' + i, x: p.x, y: p.y, html: inner, wrapFrom });
   });
 
+  // Exit ghost: a temporary head element that slides off the exit wall and fades out,
+  // giving the illusion the snake is traversing rather than teleporting.
+  if (G.wrapGhost && headHTML) {
+    const { exitFrom, exitTo } = G.wrapGhost;
+    const ghost = document.createElement('div');
+    ghost.className = 'ent notrans';
+    ghost.innerHTML = headHTML;
+    ghost.style.transform = `translate(${exitFrom.x * cell}px,${exitFrom.y * cell}px)`;
+    grid.appendChild(ghost);
+    ghost.offsetWidth; // force reflow
+    ghost.classList.remove('notrans');
+    ghost.style.transform = `translate(${exitTo.x * cell}px,${exitTo.y * cell}px)`;
+    ghost.style.opacity = '0';
+    setTimeout(() => ghost.remove(), 120);
+  }
+
   while (pool.length < ents.length) { const e = document.createElement('div'); e.className = 'ent'; grid.appendChild(e); pool.push(e); }
   while (pool.length > ents.length) { pool.pop().remove(); }
 
   ents.forEach((e, idx) => {
     const el = pool[idx];
+    if (e.wrapFrom) {
+      el.classList.add('notrans');
+      el.style.transform = `translate(${e.wrapFrom.x * cell}px,${e.wrapFrom.y * cell}px)`;
+      el.offsetWidth; // force reflow so browser registers the snap before animating
+      el.classList.remove('notrans');
+    }
     el.style.transform = `translate(${e.x * cell}px,${e.y * cell}px)`;
     el.classList.toggle('notrans', !!G.noTrans);
     if (el._html !== e.html) { el.innerHTML = e.html; el._html = e.html; }
@@ -173,7 +198,7 @@ export function helpHTML(title) {
     <div class="ov-sub" style="text-align:left;max-width:300px;">
       Eat a number, an operator, a number… to build a running total up to the <b style="color:var(--target)">MAKE</b> number — hit it and it auto-scores.<br><br>
       🔁 Only your <b>latest</b> number &amp; operator count — wrong bite? Just eat the right one next.<br>
-      🧱 Walls, your own tail, or the clock running out each cost a life.<br>
+      🌀 Hitting a wall wraps you to the opposite side — no penalty. Your own tail or the clock running out costs a life.<br>
       🌍 Climb Garden → Twilight → Inferno, where the <b>eraser</b> and <b>( )</b> unlock.
     </div>
     ${paused
diff --git a/tests/snake.test.js b/tests/snake.test.js
index 6a23cc2..884d6fc 100644
--- a/tests/snake.test.js
+++ b/tests/snake.test.js
@@ -29,20 +29,20 @@ describe('nextHead — movement', () => {
   });
 });
 
-describe('nextHead — wall collisions', () => {
-  it('returns null at right wall', () => {
-    expect(nextHead([{ x: COLS - 1, y: 5 }], { x: 1, y: 0 }, COLS, ROWS)).toBeNull();
+describe('nextHead — wall wrapping', () => {
+  it('wraps from right wall to left', () => {
+    expect(nextHead([{ x: COLS - 1, y: 5 }], { x: 1, y: 0 }, COLS, ROWS)).toEqual({ x: 0, y: 5 });
   });
-  it('returns null at left wall', () => {
-    expect(nextHead([{ x: 0, y: 5 }], { x: -1, y: 0 }, COLS, ROWS)).toBeNull();
+  it('wraps from left wall to right', () => {
+    expect(nextHead([{ x: 0, y: 5 }], { x: -1, y: 0 }, COLS, ROWS)).toEqual({ x: COLS - 1, y: 5 });
   });
-  it('returns null at top wall', () => {
-    expect(nextHead([{ x: 5, y: 0 }], { x: 0, y: -1 }, COLS, ROWS)).toBeNull();
+  it('wraps from top wall to bottom', () => {
+    expect(nextHead([{ x: 5, y: 0 }], { x: 0, y: -1 }, COLS, ROWS)).toEqual({ x: 5, y: ROWS - 1 });
   });
-  it('returns null at bottom wall', () => {
-    expect(nextHead([{ x: 5, y: ROWS - 1 }], { x: 0, y: 1 }, COLS, ROWS)).toBeNull();
+  it('wraps from bottom wall to top', () => {
+    expect(nextHead([{ x: 5, y: ROWS - 1 }], { x: 0, y: 1 }, COLS, ROWS)).toEqual({ x: 5, y: 0 });
   });
-  it('does not wrap — step just inside right wall is valid', () => {
+  it('normal move inside the grid is unaffected', () => {
     expect(nextHead([{ x: COLS - 2, y: 5 }], { x: 1, y: 0 }, COLS, ROWS)).toEqual({ x: COLS - 1, y: 5 });
   });
 });