Langton’s Loops

In 1984, Christopher Langton described a type of 2-dimensional cellular automaton that exhibits a self-replicating dynamic loop structure. A branch of Artificial Life research developed from this work, resulting in better insight into self-replicating processes, which has obvious relevance to Biology and living systems.

Below is an example of Langton’s loop. This example makes use of the LangtonsLoop class, which is an extension of the CTRBLRule class, which can be used for constructing any kind of rule based on a von Neumann neighbourhood which considers the Center, Top, Right, Bottom and Left cells explicitly.

import cellpylib as cpl

langtons_loop = cpl.LangtonsLoop()

# the initial conditions consist of a single loop
cellular_automaton = langtons_loop.init_loops(1, (75, 75), [40], [25])

cellular_automaton = cpl.evolve2d(cellular_automaton, timesteps=500,
                                  apply_rule=langtons_loop, memoize="recursive")



Langton, C. G. (1984). Self-reproduction in Cellular Automata. Physica D: Nonlinear Phenomena, 10(1-2), 135-144.