Elementary Cellular Automata are simple but powerful models used in cellular automaton theory and computational science. They consist of a grid of cells, each of which can be in one of two states: 0 or 1. The automaton evolves over discrete time steps based on a set of rules that dictate how the state of each cell depends on its current state and the states of its neighbors.

Here’s some information about Elementary Cellular Automata and Python code to simulate them:

## Elementary Cellular Automata

Elementary Cellular Automata are defined by a set of 256 rules, each corresponding to a unique binary pattern of the cell’s current state and its neighboring cells’ states. These rules determine the cell’s next state, resulting in a one-dimensional pattern that evolves over time.

- There are three components to defining a rule:
- A neighborhood size: Typically, it’s a cell and its left and right neighbors.
- A set of possible states for each cell: Binary (0 or 1) in the case of elementary automata.
- A rule table: A table specifying the next state of a cell based on its neighborhood’s current state.

### Python Code for Elementary Cellular Automaton

Here’s a Python code snippet to simulate an Elementary Cellular Automaton using NumPy and Matplotlib for visualization:

` ````
```import numpy as np
import matplotlib.pyplot as plt
def elementary_cellular_automaton(rule, num_generations, initial_state=None):
if initial_state is None:
initial_state = np.zeros(num_generations, dtype=int)
initial_state[num_generations // 2] = 1 # Initial state with a single active cell in the middle
rule_bin = np.array([int(bit) for bit in format(rule, '08b')]) # Convert rule to binary
automaton = np.zeros((num_generations, len(initial_state)), dtype=int)
automaton[0] = initial_state
for generation in range(1, num_generations):
for cell in range(1, len(initial_state) - 1):
neighborhood = automaton[generation - 1, cell - 1:cell + 2]
automaton[generation, cell] = rule_bin[np.sum(neighborhood * np.array([4, 2, 1]))]
return automaton
# Define parameters
rule_number = 30
num_generations = 50
# Simulate and visualize the automaton
automaton = elementary_cellular_automaton(rule_number, num_generations)
plt.imshow(automaton, cmap='binary', interpolation='nearest')
plt.title(f"Elementary Cellular Automaton Rule {rule_number}")
plt.show()

This code defines a function `elementary_cellular_automaton`

that takes a rule number and the number of generations as inputs and simulates the automaton. It then visualizes the automaton using Matplotlib.

You can change the `rule_number`

and `num_generations`

variables to explore different elementary cellular automata and see how they evolve over time.

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