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 netomaton as ntm
dim = (75, 75)
rule = ntm.LangtonsLoop(dim=dim)
# the initial conditions consist of a single loop
initial_conditions = rule.init_loops(1, [40], [25])
trajectory = ntm.evolve(initial_conditions=initial_conditions,
network=rule.network, timesteps=500,
activity_rule=rule.activity_rule)
ntm.animate_activities(trajectory, shape=dim)
The full source code can be found here.
For more information, see:
Langton, C. G. (1984). Self-reproduction in Cellular Automata. Physica D: Nonlinear Phenomena, 10(1-2), 135-144.