diff --git a/test/video-grid/model-test.ts b/test/video-grid/model-test.ts
new file mode 100644
index 00000000..d71fd2f5
--- /dev/null
+++ b/test/video-grid/model-test.ts
@@ -0,0 +1,247 @@
+/*
+Copyright 2023 New Vector Ltd
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+import {
+  column,
+  cycleTileSize,
+  fillGaps,
+  forEachCellInArea,
+  Grid,
+  row,
+} from "../../src/video-grid/model";
+import { TileDescriptor } from "../../src/video-grid/TileDescriptor";
+
+/**
+ * Builds a grid from a string specifying the contents of each cell as a letter.
+ */
+function mkGrid(spec: string): Grid {
+  const secondNewline = spec.indexOf("\n", 1);
+  const columns = secondNewline === -1 ? spec.length : secondNewline - 1;
+  const cells = spec.match(/[a-z ]/g) ?? [];
+  const areas = new Set(cells);
+  areas.delete(" "); // Space represents an empty cell, not an area
+  const grid: Grid = { columns, cells: new Array(cells.length) };
+
+  for (const area of areas) {
+    const start = cells.indexOf(area);
+    const end = cells.lastIndexOf(area);
+    const rows = row(end, grid) - row(start, grid) + 1;
+    const columns = column(end, grid) - column(start, grid) + 1;
+
+    forEachCellInArea(start, end, grid, (_c, i) => {
+      grid.cells[i] = {
+        item: { id: area } as unknown as TileDescriptor,
+        origin: i === start,
+        rows,
+        columns,
+      };
+    });
+  }
+
+  return grid;
+}
+
+/**
+ * Turns a grid into a string showing the contents of each cell as a letter.
+ */
+function showGrid(g: Grid): string {
+  let result = "\n";
+  g.cells.forEach((c, i) => {
+    if (i > 0 && i % g.columns == 0) result += "\n";
+    result += c?.item.id ?? " ";
+  });
+  return result;
+}
+
+function testFillGaps(title: string, input: string, output: string): void {
+  test(`fillGaps ${title}`, () => {
+    expect(showGrid(fillGaps(mkGrid(input)))).toBe(output);
+  });
+}
+
+testFillGaps(
+  "fills a gap",
+  `
+a b
+cde
+f`,
+  `
+cab
+fde`
+);
+
+testFillGaps(
+  "fills multiple gaps",
+  `
+a bc 
+defgh
+ ijkl
+mno`,
+  `
+aebch
+difgl
+monjk`
+);
+
+testFillGaps(
+  "fills a big gap",
+  `
+abcd
+e  f
+g  h
+ijkl`,
+  `
+abcd
+elhf
+gkji`
+);
+
+testFillGaps(
+  "only moves 1×1 tiles",
+  `
+  
+aa
+bc`,
+  `
+bc
+aa`
+);
+
+testFillGaps(
+  "prefers moving around large tiles",
+  `
+a bc
+ddde
+dddf
+ghij
+k`,
+  `
+abce
+dddf
+dddj
+kghi`
+);
+
+testFillGaps(
+  "moves through large tiles if necessary",
+  `
+a bc
+dddd
+efgh
+i`,
+  `
+afbc
+dddd
+iegh`
+);
+
+function testCycleTileSize(
+  title: string,
+  tileId: string,
+  input: string,
+  output: string
+): void {
+  test(`cycleTileSize ${title}`, () => {
+    expect(showGrid(cycleTileSize(tileId, mkGrid(input)))).toBe(output);
+  });
+}
+
+testCycleTileSize(
+  "does nothing if the tile is not present",
+  "z",
+  `
+abcd
+efgh`,
+  `
+abcd
+efgh`
+);
+
+testCycleTileSize(
+  "expands a tile to 2×2 in a 3 column layout",
+  "c",
+  `
+abc
+def
+ghi`,
+  `
+acc
+bcc
+def
+ghi`
+);
+
+testCycleTileSize(
+  "expands a tile to 3×3 in a 4 column layout",
+  "g",
+  `
+abcd
+efgh`,
+  `
+abcd
+eggg
+fggg
+h`
+);
+
+testCycleTileSize(
+  "restores a tile to 1×1",
+  "b",
+  `
+abbc
+dbbe
+fghi
+jk`,
+  `
+abhc
+djge
+fik`
+);
+
+testCycleTileSize(
+  "expands a tile even in a crowded grid",
+  "c",
+  `
+abb
+cbb
+dde
+ddf
+ghi
+klm`,
+  `
+abb
+gbb
+dde
+ddf
+cci
+cch
+klm`
+);
+
+testCycleTileSize(
+  "does nothing if the tile has no room to expand",
+  "c",
+  `
+abb
+cbb
+dde
+ddf`,
+  `
+abb
+cbb
+dde
+ddf`
+);