GeoPatternLab

Turmites

Two-dimensional Turing machines that draw spirals, worms and lace.

A turmite is a 2D Turing machine - its state table grows spirals, worms and lattices from one head.

About Turmites

Turmites generalize Langton's Ant into a two-dimensional Turing machine with internal states and a small transition table. Different tables grow spirals, coral, worms and intricate lattices from a single moving head. Pick a preset, run one or several turmites, and export a high-resolution PNG.

How to use Turmites

  1. Press Play. Start Turmites and watch the animation evolve in real time. Use Pause and Step to inspect it frame by frame.
  2. Adjust the rules. Use the side panel to change the parameters — the simulation responds live, so you can steer the emerging pattern.
  3. Explore variations. Press Randomize for a new starting point, or copy the share link to reproduce an exact result.
  4. Export. Pause on a frame you like and download it as a high-resolution PNG.

Frequently asked questions

What is Turmites?

Turmites generalize Langton's Ant into a two-dimensional Turing machine with internal states and a small transition table. Different tables grow spirals, coral, worms and intricate lattices from a single moving head. Pick a preset, run one or several turmites, and export a high-resolution PNG. It runs entirely in your web browser on GeoPatternLab, free and with no sign-up.

Is Turmites free to use?

Yes. Turmites on GeoPatternLab is completely free, with no sign-up or download required. Create as much art as you like and export it directly from your browser.

How do I download my Turmites artwork?

Use the export buttons in the toolbar to save your work as a high-resolution PNG image. Files download straight to your device.

Does Turmites work on phones and tablets?

Yes. Turmites is fully responsive and works with touch input on phones and tablets as well as with a mouse or trackpad on desktop.

Can I use Turmites artwork commercially?

Yes. Artwork you create with Turmites is yours to use for personal and commercial projects, such as wallpapers, prints, textiles, and teaching materials. See our Terms of Use for full details.

Related tools

Explore more free pattern generators and geometric art tools on GeoPatternLab:

  • Cellular Automata — Elementary cellular automata woven into intricate row-by-row patterns.
  • Game of Life — Conway's Game of Life and other life-like cellular automata, animated live.
  • Brian's Brain — A three-state cellular automaton that erupts into shifting, spark-like waves.
  • Cyclic Cellular Automata — Colorful cyclic automata that self-organize into rotating spirals.
  • Langton's Ant — A tiny ant that turns on colors and builds surprising highways.
  • Wireworld — A four-state automaton for simulating electrons racing through circuits.

Browse all 48 tools.