How it works
Every step replaces each of the nine hexagon types (G D J L X P S F Y, the paper's Γ Δ Θ Λ Ξ Π Σ Φ Ψ) with seven or eight smaller ones. At the bottom, each hexagon becomes one Spectre, except G, which becomes two: the second is turned 30°, the only odd orientation in the tiling.
A Spectre's coordinates list which child it is of which hexagon, all the way up. Walking across an edge usually rewrites only the lowest one or two of them. Seeds that contain themselves make each patch sit exactly inside the next, so adding a step grows the tiling outward around what you are looking at.
Positions are exact. Each vertex is a₀ + a₁d + a₂d² + a₃d³ with integer coefficients and d = eiπ/6. Curved edges bulge out on even edges and in on odd ones; every shared edge still matches, which is the odd-to-even rule that makes the tile strongly chiral.
The tile studio paints one Spectre. Every tile in the patch reuses that painting, moved and turned to fit, and the turned G halves can carry a design of their own. Your design stays in this browser.
Sources: A chiral aperiodic monotile (Smith, Myers, Kaplan, Goodman-Strauss, 2023) and Simon Tatham's Combinatorial coordinates for the aperiodic Spectre tiling. Hexagon letters, child numbers and edge numbers follow Tatham.
Spectre Lab v1.9.0 (build bc4c2ea) is open source under the MIT License. The README and source code are on GitHub. If you enjoy it, you can support Spectre Lab with whatever you like.