cellular automaton

( >> Ata, Horos)

A cellular automaton is a discrete model, which means that they don’t require the notion of continuity. Cellular automata have many applications in mathematics, computation and biology. A cellular automaton consists of a grid where each cell may have two states, empty of full (0 or 1) and a specific set of rules that defines the way that the state of the cells is changing over time. After the rules are applied to all the cell of the grid a new generation is created. Those rules are always in relation to the neighbor cells of each cell. That is the state of each cell in generation n is defined by the state of its neighbor cells in generation n-1. One of the most famous set of rules is Conway's Game of Life:
1. Any live cell with fewer than two live neighbors dies, as if by loneliness.
2. Any live cell with more than three live neighbors dies, as if by overcrowding.
3. Any live cell with two or three live neighbors lives, unchanged, to the next generation.
4. Any dead cell with exactly three live neighbors comes to life.

One of the most interesting properties of the cellular automaton is that it requires no input from the user (therefore an automaton). It is a self referential process where the output of each generation is becoming the input for the next one. What is also interesting is that from a very specific and simple set of rules, when we let the automaton to evolve, we can produce very complex formations.

Xenakis used cellular automata in many of his later works, for example Ata and Horos, in order to create new harmonic progressions.






(the following animation uses the life.mel script from nthd.org)