One-Dimensional Cellular Automata with Memory

α-type memory, d=1 r=1,2

time steps

25

memory weight α

0.5

radial neighborhood

1

2

rule number

30

initial conditions

one seed

random

perturbation analysis

off

on

majority memory, d=1 r=1,2

time steps:

25

memory size τ:

1

radial neighborhood

1

2

rule number:

30

initial conditions:

one seed

random

perturbation analysis

off

on

steps: 25 α: 0.5 rule number: 30

steps: 25 τ: 1 rule number: 30

This Demonstration shows an implementation of memory in one-dimensional cellular automata. We use two kinds of memory mechanisms (average

α

-type memory and majority memory) to first determine the cell trait states, based on their past states, and then apply the formally unchanged updating rule. Average memory acts by means of a weighting mechanism based on a memory factor

0⩽α⩽1

. Majority memory acts by selecting the most frequent of the last

τ

states. Both types of memory are shown simultaneously for comparison. Initial states can be chosen between one single seed or a random set. Perturbation analysis may also be visualized.