A Factorio mod that carves every planet into cells of an aperiodic tiling.
Your factory is built on the "hat" monotile tiling — the aperiodic tiling discovered in 2023. Cells never repeat, so neither can your blueprints.
Status: released as 0.1.0, on the mod portal and as a GitHub release. Multiplayer is unverified — the determinism argument is sound but has never been confirmed with two clients, so play single player for now.
Each cell is a hat, separated from its neighbours by a narrow unbuildable band. You can walk and drive across a band, and underground belts and pipes tunnel beneath it, but nothing can be built on one.
That single rule changes how you build:
- Imported blueprints stop working. Not because of rotation — because every cell is a genuinely different shape. Over 1,156 cells measured at the default settings there are 885 distinct buildable tile shapes, and no single one covers more than 0.5% of the map. A layout that fills one cell will not fit the next.
- Small blueprints still travel. Anything up to 17×17 at the default settings fits every cell. Assembler clusters are fine; a 30×30 mall is not.
- Every connection between cells is a puzzle. Belts cross by underground pair, against an edge that is never axis-aligned.
The result is a factory that has to be fitted to the ground it sits on.
Per planet, set at world creation.
| Setting | Default | Choices |
|---|---|---|
| Cell size (centre to vertex, tiles) | 41 (normal) | 15, 26, 41, 52 |
| Band width (tiles) | 3 (wide) | 1, 2, 3, 4 |
| Band appearance | Dark liquid | liquid, void |
| Band colour | Deep violet | violet, cold, oily, ember, void black |
Hat size is the dial that matters. It decides how much room you get and how large a blueprint survives:
At the default band width of 3:
| size | difficulty | cell area | reusable blueprint | preview |
|---|---|---|---|---|
| 15 | very hard | 63 t | 5×5 | look |
| 26 | hard | 294 t | 10×10 | look |
| 41 | normal | 858 t | 17×17 | look |
| 52 | easy | 1,473 t | 22×22 | look |
Changing the setting later affects only newly created surfaces; existing ones keep the geometry their terrain was built with, so nothing ever seams.
Factorio's grid is not a rendering choice — tiles, collision, belt lanes, pipes and the pathfinder are all C++ and all assume axis-aligned 1×1 tiles. No mod can make the unit of construction hat-shaped. What a mod can do is decide where you may build, and that turns out to be enough.
Generating the tiling is the interesting part. It is aperiodic, so there is no lattice to snap to and no period to exploit; the mod computes which hats overlap a chunk by descending a substitution tree, pruned by bounding circle, at about 0.7 ms per chunk.
If you like that sort of thing, the wiki has a write-up — how the limiting metatiles were recovered as exact algebraic numbers, and why plain doubles beat exact integer arithmetic by nine orders of magnitude.
hat/ the tiling core — no Factorio dependencies, runs under plain Lua
tools/ offline pipeline (Python) that derives and verifies the rule data
data/ generated Lua data; never edit by hand
spec/ busted tests
docs/design/ the design spec, including everything that turned out wrong
Requires Lua 5.2 (the version Factorio embeds), busted and luacheck:
sudo pacman -S --needed lua52 lua52-busted luacheck # Arch
make check # Python + Lua tests + lint
make data # regenerate data/ and test fixtures
lua5.2 tools/render.lua 5 12 340 out.svg # draw the tiling
lua5.2 tools/render_bands.lua 26 2 260 bands.svg # preview in-game lookThe core is validated against a golden fixture exported from the Python pipeline, which is itself checked for overlaps, gaps, correct reflected-hat density, and hat counts matching F(2n+3)².
The hat monotile was discovered by David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss (2023). The substitution structure here is derived from Kaplan's hatviz (BSD-3-Clause) — see THIRD_PARTY.md.
Hextorio solved several of the same problems for hexagons first, and its approach to storing geometry per surface is borrowed here.
MIT licensed.