Multiscale Truchet Tiles

Truchet tiles at every size from fourteen cells down to one, packed largest first into a forty-eight-cell grid.

Truchet at several scales

A Truchet tile carries a motif that meets its own edges at fixed points, so that neighbouring tiles join whatever their orientation. This piece takes that further: the tiles are not all the same size.

Tiles run from MaxSize cells square down to one, and because every size meets its edges at the same proportional points, a ten-cell tile joins a one-cell tile as cleanly as it joins another ten-cell tile.

Step 01

The largest tiles. The placement is dart-throwing: pick a random cell, test whether a tile of the current size fits there, and place it if so.

Down the size ladder

int size = Math.Min(MaxSize, Dimension);
bool done = false;
while (!done)
{
    int tries = RndAttempts;
    …
    if (!placed)
    {
        if (size == 1) { /* fill every remaining cell */ done = true; }
        else size--;
    }
}

RndAttempts failed throws in a row is taken as evidence that no more tiles of this size will fit, and the size drops by one. That is a probabilistic stopping rule, not a proof — occasionally a gap that would have fitted is missed, and the piece is better for it, because a perfect pack at each size would leave a suspiciously regular remainder.

At size one the rule changes: rather than throwing darts, every remaining empty cell is filled exhaustively. The tiling is therefore always complete.

Step 02

A little over a tenth of the tiles.

Step 03

Nearly a third. The joins across tiles of different sizes are visible now, and they are seamless — an arc leaving a large tile at its edge midpoint is met by an arc entering a small one at the same point.

Step 04

Three fifths. Note how far down the size ladder that gets: most of the count is in the small tiles, because each size step leaves gaps that the next size fills several times over.

Step 05

Complete.

Curved or straight

public float PCurved { get; init; } = 1f;

Each tile takes a quarter-arc motif with probability PCurved and a straight-line motif otherwise. At 1 every tile is curved and the whole piece reads as woven cord; drop it and straight segments break the curves into a mixture of rope and lattice.

Five renderings

Rendering	Grid	Max tile	Structure	Palette
Cobalt Monoliths	48	14	broad nested arcs	ice blue on deep navy
Vermillion Switchyard	56	9	arcs, rails and inset tile frames	vermillion on warm paper
Violet Tides	42	11	pinched fixed Bézier curves	lilac on aubergine
Copper Cells	72	6	dense mixed motifs and cells	copper on forest-black
Acid Ribbons	34	13	variable sweeping Bézier curves	acid yellow on charcoal

Dimension and MaxSize together decide the range of scales in the piece: a large grid with a small maximum gives a near-uniform texture, and the reverse gives a few dominant tiles surrounded by filler.

Determinism

The generator is seeded from the preset and consumed by the dart-throwing and by each tile’s motif choice, in placement order. The exhaustive fill at size one consumes it in grid order. Same seed, same tiling.

Progression 05

Variant 05