Cellular Automaton Discrete Model

A Cellular Automaton is a discrete model similar to any other automaton which has its own start state(s) and a set of rules. 

A cellular automaton is a model of a system of "cell" objects with the following characteristics :

• The cells live on a grid which can be either 1D or even multi-dimensional
• Each cell has a state. The number of state possibilities is typically finite. The simplest example has the two possibilities of 1 and 0
• Each cell has a neighbourhood and it is typically a list of adjacent cells

The working principle of the cellular automata is shown below:

1. An initial state is selected by assigning a state for each cell.
2. A new generation is created, according to some fixed rule that determines the new state of each cell in terms of:
   • The current state of the cell.
   • The states of the cells in its neighbourhood.
3. Hence, a new state is calculated by looking at all previous neighbouring states.

1. Conway’s Game Of Life

2. Rule 90:

Rule 90 is an elementary cellular automaton that consists of a one-dimensional array of cells, each of which can hold either a 0 or a 1 value. Each cell is the exclusive or(XOR) of its two neighbours. 

If we concatenate the Next State into a single binary number and convert it to decimal (01011010)_2, it becomes 90, hence we get the name Rule 90. 

3. When the initial state has a single nonzero cell, this diagram has the appearance of the Sierpiński triangle. 

Implementation of Sierpiński triangle:

The rules of Rule 90 Cellular Automata are as follows: 
 Rule 1: 0 0 0 -> sets cell to: 0
 Rule 2: 0 0 1 -> sets cell to: 1
 Rule 3: 0 1 0 -> sets cell to: 0
 Rule 4: 0 1 1 -> sets cell to: 1
 Rule 5: 1 0 0 -> sets cell to: 1
 Rule 6: 1 0 1 -> sets cell to: 0
 Rule 7: 1 1 0 -> sets cell to: 1
 Rule 8: 1 1 1 -> sets cell to: 0

 SIERPINSKI TRIANGLE

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