Two aperiodic monotiles, one page. The hat (with its continuous Tile(a, b) family, from the hat through the equilateral to the turtle) tiles only with the help of mirror copies; the spectre tiles with a single handedness and no mirrors at all. The switch keeps the seed, the colour scheme, the highlight, and the view, so you can flip between the two worlds in place. The two substitution systems are different — H, T, P, F metatiles for the hat, nine Greek-lettered clusters for the spectre — so the pictures rearrange rather than morph.
The hat family carries the shape presets: hat (1, √3), turtle (√3, 1), the equilateral (1, 1), or custom a and b. The spectre carries the curve slider instead: 0 is the straight-edged Tile(1, 1) — the very shape the equilateral preset shows in the hat family, tiled the spectre way — and 1 is the full spectre. Everything else works as on the hat page and the spectre page, where the two families are explained in full.
All schemes work in both families. reflection shows the hat's mirrors and is
one colour for the spectre (nothing to show — that is the spectre's point);
mystic shows the spectre's odd-rotation companions and is one colour for the hat.
meta colours four metatile types in the hat family and nine in the spectre.
Mathematics: An aperiodic monotile and A chiral aperiodic monotile. Built in Rust, compiled to WebAssembly; source on GitHub.