GenerateRandomSearch

Tessellation Generator

A tiling is only a tiling if it leaves no gaps and no overlaps, and that is easy to claim and easy to get subtly wrong at the edges. This tiles a grid three ways — plain squares, offset bricks, and dominoes found by search — and then checks every single cell for exactly one covering tile. The domino case also demonstrates something the pattern cannot: a grid with an odd number of cells has no tiling at all, however you arrange them.

What this generator does

Covers a grid with the tile shape you choose. Squares and bricks follow a fixed pattern; dominoes are found by backtracking search. Every cell is then checked to belong to exactly one tile, and each tile's cells are confirmed to be adjacent.

How to use this tool

  1. Choose a tile shape and the size of the grid.
  2. Generate, and look at the coloured tiles covering the grid.
  3. Try dominoes on a grid with an odd number of cells.
  4. Use a seed to reproduce the same domino arrangement.

Understanding the controls

Tile shape
Squares cover trivially. Bricks offset alternate rows, so odd rows start and end with a half brick. Dominoes cover two adjacent cells each and need a search rather than a pattern.
Grid width and height
Between 2 and 16 each. For dominoes, the product matters: an odd number of cells can never be tiled, and the tool says so rather than producing a nearly complete covering.
Seed
Reproduces the same domino arrangement, since the search makes random choices between placing a tile across or down.

Common use cases

  • Producing tiling patterns for a design or classroom display
  • Showing why an odd grid cannot be tiled by dominoes
  • Generating domino tiling puzzles with a known solution
  • Teaching what \u201ccovers with no gaps or overlaps\u201d actually requires
  • Making brick-pattern layouts with correct half tiles at the row ends

How this generator works

Squares and bricks follow their pattern directly, with the brick rows offset by one cell so alternate rows begin with a half tile. Dominoes are placed by backtracking: the first uncovered cell in reading order is paired either rightwards or downwards, and the search backs up whenever it reaches a dead end. An odd number of cells is rejected immediately, since each domino covers two and no arrangement can reach an odd total. Before display every cell is checked for exactly one covering tile, and every tile's cells are confirmed to be genuinely adjacent.

Randomness and fairness

Uses your browser's cryptographic random source to choose between placing each domino across or down. A seed reproduces the same arrangement, deterministically and not cryptographically securely.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

  • Tiles are grid-aligned rectangles, so triangular, hexagonal and irregular tilings are outside what this covers.
  • The domino search finds one tiling, not all of them — a large grid has an enormous number, and counting them is a separate problem.
  • Brick rows are offset by exactly one cell, so other offsets like a third-bond pattern are not available.
  • The display colours tiles by index, so two distant tiles can share a colour on a large grid.

Privacy and your data

The tiling is computed in your browser and nothing you choose is transmitted, stored or included in analytics.

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