"What are cellular automata?"

Cellular automata are a type of algorithm that work with a grid of cells that have a state . And the state of these cells changes based on the cells around it. One of the most famous cellular automaton would be Conway's game of life or CGoL.

Conways game of life.

CGoL is known for it's life like motion over time. CGoL created in 1970 by British mathematician John Horton Conway. The rules of CGoL are simple:

Each cell looks at it's neighbors. A cell is white if it is dead and black if it is alive. A cell needs 2 or 3  live neighbors to stay alive. If a dead cell has 3 live neighbors it becomes a live cell. Applying these rules every step results in something that looks very life like.

Rule 30

Fast forward to 1983 and Stephen Wolfram introduces rule 30 a very chaotic cellular automaton. Rule 30 works as shown in this picture:

Rule 30 is a great example of emergence. From the simple rules that it has come very random looking patterns.

Conclusion

In conclusion, cellular automata are a fascinating type of algorithm with all sorts of possibilities. There are too many cellular automata to cover them all. But these two would be the most well known for sure.