Islamic Geometry Explorer

Based on the classic eight-fold rosette pattern. Construction drawn from Daud Sutton's book "Islamic Design: A Genius For Geometry."

Click a line to toggle it (and its symmetric copies); click a tile to recolour it. Every variant stays radially symmetric (D4) and tiles seamlessly — loose ends, including at tile edges, are trimmed automatically. Start from the full straightedge-and-compass construction and carve out a pattern. Keys, so you can stay on the drawing: R random, B back, F forward.

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adds lines +  ·  removes individual lines  ·  hides the whole pattern when it fails the test

Pattern source (SVG) — load your own pattern, or edit and reload
units Load replaces the whole pattern with every <line> in the box — select-all and paste to use your own.

Unit cell

Tiled (3 × 3)

The cell repeats by translation; lines run continuously across cell edges.
Single-stroke path — draw every line in one continuous stroke, without crossing

Finds one continuous path that covers every line above, end to end, exactly once — and never crosses itself: at each intersection the path turns rather than running straight through. (An "A-trail", to give it its name.) For that to be possible, every junction needs an even number of lines meeting it, so the path can always arrive and leave again. Two odd junctions are also fine — they become the two ends of the stroke. A line that just stops in the middle of the pattern can never work; one that stops at the cell edge can, and the two boxes below are the two ways to handle it. They change this solver only: Only single path above keeps showing just the patterns that trace on their own. Solves whatever is drawn right now — carve the pattern above, then Re-solve.

Loose ends at the cell edge, for this solver only —
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1.5 1.0
2.0 circle