# Cellular Automata

## What is it?

- The cells live on a
**grid**. - Each cell has a
**state**. The number of state possibilities is typically finite. ( usually off and on ) - Each cell has a
**neighborhood**. This can be defined in any number of ways, but it is typically adjacent cells.

## Stanisław Ulam

Studying growth of crystals

## John von Neumann

Imagining a world of self-replicating robots.

# A New Kind of Science

## Stephen Wolfram

Discusses how CA are not simply neat tricks, but are relevant to the study of biology, chemistry, physics, and all branches of science.

# What is the simplest cellular automaton we can imagine?

# Elementary CA

**Grid.** The simplest grid would be one-dimensional: a line of cells.

**States**. The simplest set of states would be two states: 0 or 1.

**Neighborhood**. The simplest neighborhood in one dimension for any given cell would be the cell itself and its two adjacent neighbors: one to the left and one to the right.

# Time

# Generations

`CELL state at generation = f(CELL, neighbourhood at (generation - 1))`

# Blurring an image

## A pixel’s new state (i.e. its color) is the average of all of its neighbors’ colors.

# For Example

## A cell’s new state is the sum of all of its neighbors’ states.

# Another Example

# Wolfram’s elementary CA

## Look at all the possible configurations of a cell and its neighbour and define the state outcome for every possible configuration.

# Seems ridiculous?

# We have three cells

## How many possible ways can we configure the states?

# Three cells define a 3 bit number

How high can you count with 3 bits?

Up to 8

# Once we have defined all the possible neighborhoods,

# we need to define an outcome (new state value: 0 or 1) for each neighbourhood configuration.

# Standard Wolfram Model

#### Cellular Automata

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