Resources and tools
Generators, datasets, museums, fabrication files, OEIS sequences, and built installations.
How to use this index
The numbered bibliography holds peer-reviewed and preprint research with stable citation anchors. This page catalogs everything else: official generators, open fabrication files, museum exhibits, workshop kits, games, OEIS sequences, journalism, and documented installations.
Tile(1,1) is not the same as Spectre. The straight-edged Tile(1,1) polygon admits a periodic tiling if reflected copies are mixed; Spectres are edge-modified, strictly chiral shapes. Many community repositories reuse the word “Spectre” for straight-edged outlines — verify the geometry before fabrication.[2]
An automated crawl maintains a machine-readable source registry for literature discovery. The lists below are human-curated and tiered: link freely, but check each site’s license before republishing assets.
Catalog
Official project pages and discoverer accounts
- Kaplan, Aperiodic Monotiles — discovery chronology and community links
- David Smith, Hedraweb — discoverer blog and physical experiments
- David Smith, The Special One — first-person Tile(1,1) / Spectre story
- Joseph Myers — publications and preprints
- Chaim Goodman-Strauss — papers and notes
- Combinatorial Theory — Hat paper (open access)
- Combinatorial Theory — Spectre paper (open access)
Generators, code, and datasets
- isohedral/hatviz — official Hat patch builder (BSD-3-Clause)
- isohedral/hatvalidate — computer-assisted aperiodicity verification
- henningle/TileOneOne — reference Tile(1,1) MATLAB generator (MIT)
- jsm28/AperiodicMonotilesLean — Lean formalization staging repo
- reversi-fun/symbolic-spectre-tiles — symbolic coordinates and CSV/SVG export (MPL-2.0)
- ctkrug/monotile — infinite Spectre pan/zoom studio
- Ricky Reusser — WebGPU aperiodic monotile rendering notebook
- Ricky Reusser — deep-zoom aperiodic monotile notebook
- James Smith — AperiodicCube 3D interactive demo
- Simon Tatham — coordinate algorithms for Hat tilings
- Simon Tatham — finite-state transducers for Hat and Spectre
- Simon Tatham — refinable frontier (H7/H8 and Spectre hex types)
- Jaap Scherphuis — PolyForm Puzzle Solver (discovery-era search tool)
- Spectre Tiling Playground — manual editor with TILE coordinate format
- Beach Spectre Practise — touch-friendly substitution trainer
Institutional references and OEIS
- Tilings Encyclopedia — Hat substitution record
- Tilings Encyclopedia — CAP representative
- Tilings Encyclopedia — aperiodic monotile glossary
- OEIS A363445 — Hat perimeter fractal turn sequence
- OEIS A397115–A397123 — Spectre hierarchical cluster counts (2026)
Museums, competitions, and workshops
- UKMT Einstein Mad Hat Awards — competition archive
- Hatfest — Oxford / Grimm Network conference archive
- Cambridge Faculty of Mathematics — Tip of the Hat celebration
- Marcello Seri — Spectres, Hats and Maths workshop kits (CC BY 4.0)
- Bridges 2024 — Group activity to build a Spectre tiling
- Numberphile — Discovery of the Aperiodic Monotile
- Quanta — Hobbyist finds maths elusive Einstein tile
Fabrication, installations, and products
- Beach Spectres — public sand-tiling project and how-to guides
- Printables — Einstein Tiles family (Hat, Tile(1,1), Spectre variants)
- Spirko/SpectreOpenSCAD — parametric Spectre STL generator (GPL-3.0)
- vmagnin/hat_polykite — laser-cut Hat and Tile(1,1) sheets
- Nervous System — wooden Spectre puzzle (111 pieces)
Curated quick links
- Kaplan et al., An aperiodic monotile project page — interactive patch builders, source code, and CC BY sample images
- Kaplan et al., A chiral aperiodic monotile project page — Tile(1,1) patch app and Spectre SVG outlines for cutting and printing
- christianp/aperiodic-monotile — OpenSCAD, STL, and SVG files for fabricating Hat, Turtle, and Spectre tiles
- Printables: Spectre chiral aperiodic monotile — parametric 3D-printable tiles with this-way-up orientation grids
- National Museum of Mathematics: The Hat and the Spectre — exhibits and the Einstein Mad Hat competition
- Nan Ma, aperiodic-monotile-4d — original Wolfram Language code and projection experiments (no license; link only)
- Arnaud Chéritat and Nan Ma, interactive 4D projection applet — CC BY-SA
- Simon Tatham, Combinatorial Coordinates for the Aperiodic Spectre Tiling
- Christian Lawson-Perfect et al., multi-format monotile assets — CC0 SVG, DXF, OpenSCAD, and STL
- Infinite Spectres — MIT-licensed Rust/WebGPU deep-zoom viewer
- Tilings Encyclopedia: Spectre — institutional patch and reference record
- Large Spectre Tiling — 488-piece hierarchical group activity
- Terracing with Spectres — built CNC-waterjet limestone terrace and process archive
- Hats in Grout — practical fabrication and installation geometry
- OEIS A363348 — recursive turn sequence for drawing an infinite Hat tiling
Still missing?
No single index can guarantee completeness on the open web. If you maintain a generator, dataset, fabrication guide, or installation archive that belongs here, contact us with a URL, license, and one-line description.
See also
Bibliography, Education, Materials and fabrication
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