Step by Step solution about How to resolve the algorithm One-dimensional cellular automata step by step in the Mathematica / Wolfram Language programming language

Code Explanation:

The code generates and displays cellular automata patterns using Wolfram's programming language.

Cellular Automata:

Cellular automata are systems of cells that update their states based on the states of their neighboring cells. Each cell has a state (e.g., 0 or 1) and follows a set of rules to determine its next state.

Code Breakdown:

1. Rule Definition:

CellularAutomaton[{{0,0,_}->0,{0,1,0}->0,{0,1,1}->1,{1,0,0}->0,{1,0,1}->1,{1,1,0}->1,{1,1,1}->0},...

This defines the rules for the cellular automata. The syntax {{state1, state2, state3}->newState} means that if a cell has state state1 to its left, state state2 at its current position, and state state3 to its right, then its next state will be newState. The _ symbol represents any state.

2. Initial State and Number of Iterations:

{{1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1},0},12

This specifies the initial state of the cellular automata as a list of 0s and 1s. The second parameter, 12, indicates the number of iterations.

3. Displaying the Patterns:

Print @@@ (% /. {1 -> "#", 0 -> "."});

This converts the cellular automata output (a list of 0s and 1s) into a grid of characters. 1 is replaced with "#" (a hash symbol) to represent a filled cell, and 0 is replaced with "." (a period) to represent an empty cell. The resulting grid is then printed.

4. Additional Example:

The following code generates a different cellular automata pattern with a different rule:

CellularAutomaton[2^^01101000 (* == 104 *), {{1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1}, 0}, 12];

This pattern is often referred to as "Rule 104."

CellularAutomaton[{{0,0,_}->0,{0,1,0}->0,{0,1,1}->1,{1,0,0}->0,{1,0,1}->1,{1,1,0}->1,{1,1,1}->0},{{1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1},0},12]
Print @@@ (% /. {1 -> "#", 0 -> "."});


CellularAutomaton[2^^01101000 (* == 104 *), {{1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1}, 0}, 12];


###.##.#.#.#.#..#
#.#####.#.#.#....
.##...##.#.#.....
.##...###.#......
.##...#.##.......
.##....###.......
.##....#.#.......
.##.....#........
.##..............
.##..............
.##..............
.##..............
.##..............