Book a Demo!
CoCalc Logo Icon
StoreFeaturesDocsShareSupportNewsAboutPoliciesSign UpSign In
Download

A (one dimensional) cellular automaton is a function1 F : Σ → Σ with the property that there is a K > 0 such that F (x)i depends only on the 2K + 1 coordinates xi−K , xi−K+1, . . . , xi−1, xi, xi+1, . . . , xi+K . A periodic point of σ is any x such that σ^p (x) = x for some p ∈ N, and a periodic point of F is any x such that F^q (x) = x for some q ∈ N. Given a cellular automaton F, a point x ∈ Σ is jointly periodic if there are p, q ∈ N such that σ^p (x) = F^q (x) = x, that is, it is a periodic point under both functions.

This project aims to explore the nature of one-dimensional Cellular Automata, in the hope of finding the structure of cellular automata through its periodic points.

2037 views
License: MIT
ubuntu2004
Tweet
Share
Share
1
import tomato as tt

2
from tomato.functions import utils

3
import moore_fractal as rule

4
import numpy as np

5


6
def point_matrix(size, value):

7
    """

8
    Creates an array of zeros with an element of specified value not medium.

9
    """

10
    try:

11
        m, n = size

12
    except TypeError:

13
        m,n = size, size

14
    

15
    

16
    state_matrix = np.zeros((m,n))

17
    state_matrix[m // 2, n // 2] = value

18
    

19
    return state_matrix

20


21
cell_size = 4

22
dimensions = 150

23


24
state_matrix = point_matrix(dimensions, 1)

25


26
board = tt.Board(rule, cell_size=cell_size)

27
board.start(state_matrix)

28


29


30


31