Wolfram=20 one-dimensional cellular automata
The mathematician Stephen Wolfram created a = one-dimensional=20 variation of von Neumann's cellular automata which develops on a=20 one-dimensional universe (a line). In this type of CA, each cell is = surrounded=20 by only two other cells, its two immediate neighbors on either side. = Each=20 succeeding generation is represented by a line underneath the = preceding one. A=20 cell in generation 2 determines its state (dead or alive) by looking = at the=20 state of the cell directly above it (that is, in generation 1) and at = that=20 cell's two neighbors. There are only eight possible combinations of = the states=20 of those 3 cells, ranging from "AAA" (all alive) to "DDD" (all dead). = Since=20 there are only eight possible states for the ancestors of any given = cell, and=20 these states may result in one of two states for the new cell (dead or = alive),=20 there are 256 (2 to the 8th power) possible rulesets for this type of = cellular=20 automata. Wolfram classified all 256 rules in four different = "classes":
Class I are rules that generate boring configurations, = such as all=20 dead or all alive cells.
Class II includes "frozen" configurations, where all = initial=20 activity eventually settles down to stable structures.
Class III rules generate chaotic = configurations,=20 resembling noise patterns.
Class IV rules display complex but not random behavior. = The output=20 is highly sensitive on initial conditions (cell configuration). =
These=20 universes are one-dimensional tori, that is, the last cell connects = with the=20 first cell. It is remarkable how the aural representation resembles = the=20 graphical output of these CA. You can very clearly hear the = differences=20 between all four classes and how they match perfectly with their = graphical=20 counterpart.