Multicolored Turmites

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

This Demonstration is an animation of single-state, multicolor, 2-dimensional Turing machines, also known as turmites [1, 2]. Langton's ant is the most famous turmite.


An "ant" moves on a grid one cell at a time. The cells can have one of colors to . When the ant arrives at a cell with color , it changes its color cyclically to and turns either left, right, forward, or backward according to a list of rules , one for each color. At the borders of the grid, the ant wraps around cyclically.

Starting from a gray colored grid and with the ant in the center, this Demonstration moves the ant step by step according to the rules for colors that can be set by the togglers (right, left, forward, u-turn, none), with values (-1, 1, 0, 2, Null). You can vary the number of colors (between 2 and 8) by setting some togglers to "none".


Contributed by: Erik Mahieu (December 2013)
Open content licensed under CC BY-NC-SA




[1] S. Wolfram, A New Kind of Science, Champaign, IL: Wolfram Media, Inc., 2002. (Dec 17, 2013) p. 185 (NKS|Online) and notes for Chapter 5, pp. 930–931 (NKS|Online).

[2] E. Pegg Jr. “Math Games: 2D Turing Machines.” Mathematical Association of America. (Dec 17, 2013) 07_ 04.html.

[3] T. Hutton. “Two-Dimensional Turing Machines.” (Dec 17, 2013)

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.