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.
adds lines + · removes individual lines − · hides the whole pattern when it fails the test ⊘
<line> in the box — select-all and paste to use your own.
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.