Turmites

A simple N-state two-color Turing machine which operates on a wrapped grid of black and white cells, and follows custom rules on every tick of a clock.

See http://turmites.destructuring-bind.org for a running example. By default one ant is automatically created; Extra ants may be added by clicking on the canvas.

Rules may be specified by adding a rule=... parameter, of which some permissible values are shown below.

• langtons-ant (which has an implicit rule of 120080)

• coiled-rope (implicit rule: 111180121010)

• computer-art (implicit rule: 180121020081)

• fibonacci (implicit rule: 181181121010)

• worm-trails (implicit rule: 121181121020)

• striped-spiral (implicit rule: 021080181020)

A full list of pre-defined rules can be found here. If no rule is given, then a pre-defined one will be selected at random. Or, alternatively, the rule definitions may be specified as a sequence of numeric digits, eg. http://turmites.destructuring-bind.org/?rule=021080181020

An N-state two-color rule consists of 2N triples, {a,b,c}, where:

• a: the new color of the square

• b: the direction(s) for the turmite to turn

• c: the new internal state of the turmite

For example, the fibonacci turmite, has rule definition 181181121010 has two states and two colors, and is split into four triples {1,8,1}, {1,8,1}, {1,2,1} and {0,1,0}. The particulat triple is selected based on the current state and the current color. The {1,8,1} triple therefore states that the colour should change to 1, turn left (8) and adopt state 1 before moving forwards.

The direction to turn is specified by:

• 1: no turn

• 2: right

• 4: u-turn

• 8: left

The actions are specified by a state transition table listing the current internal state of the turmite and the color of the cell it is currently standing on. For example, the next rule-set to use for the fibonacci triples shown above are used by the following table:

                          current-color = 0    current-color = 1
current-state = 0              1,8,1                1,8,1
current-state = 1              1,2,1                0,1,0

So if the current state is 1 and the current color is 0, then the {1,2,1} triple is selected and the new color, direction and state are derived from that.

Building and Running

Invoke a noir instance using leiningen:

$ lein run

The clojure script will compiled down to javascript as part of the build, so browse to http://localhost:8080

Editing Code

Don't try to edit the javascript - it is compiled from ClojureScript in src/turmites/client/core.cljs using Leiningen with the lein-cljsbuild plugin:

$ lein cljsbuild clean
$ lein cljsbuild auto

Refresh the page in the browser after having saved the file and allow for the compilation phase to complete.

Notes

Turmites are a generalization of Langtons-ants.

Inspired (in part) by Stephen Wolfram's, "A New Kind of Science", ISBN 1-57955-008-8

References

• http://www.maa.org/editorial/mathgames/mathgames_06_07_04.html

• http://code.google.com/p/ruletablerepository/wiki/TwoDimensionalTuringMachines

• http://demonstrations.wolfram.com/Turmites/

• https://en.wikipedia.org/wiki/Turmite

• http://golly.sourceforge.net/

License

Copyright (c) Richard Hull 2012

Same as the eclipse public license - v 1.0: https://www.eclipse.org/legal/epl-v10.html