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Rule 30 is an elementary cellular automaton introduced by Stephen Wolfram in 1983. [2] Using Wolfram's classification scheme , Rule 30 is a Class III rule, displaying aperiodic, chaotic behaviour. This rule is of particular interest because it produces complex, seemingly random patterns from simple, well-defined rules.
Examples are rules 4, 108, 218 and 250. Class 3: Cellular automata which appear to remain in a random state. Examples are rules 22, 30, 126, 150, 182. Class 4: Cellular automata which form areas of repetitive or stable states, but also form structures that interact with each other in complicated ways. An example is rule 110.
The rule 30, rule 90, rule 110, and rule 184 cellular automata are particularly interesting. The images below show the history of rules 30 and 110 when the starting configuration consists of a 1 (at the top of each image) surrounded by 0s.
When used on their own without such context, the codes are often assumed to refer to the class of elementary cellular automata, two-state one-dimensional cellular automata with a (contiguous) three-cell neighbourhood, which Wolfram extensively investigates in his book. Notable rules in this class include rule 30, rule 110, and rule 184.
The most famous examples in this category are the rules "Brian's Brain" (B2/S/3) and "Star Wars" (B2/S345/4). Random patterns in these two rules feature a large variety of spaceships and rakes with a speed of c, often crashing and combining into even more objects. Larger than Life is a family of cellular automata studied by Kellie Michele Evans ...
A cellular automaton is defined by its cells (often a one- or two-dimensional array), a finite set of values or states that can go into each cell, a neighborhood associating each cell with a finite set of nearby cells, and an update rule according to which the values of all cells are updated, simultaneously, as a function of the values of their neighboring cells.
In von Neumann's cellular automaton, the finite state machines (or cells) are arranged in a two-dimensional Cartesian grid, and interface with the surrounding four cells. As von Neumann's cellular automaton was the first example to use this arrangement, it is known as the von Neumann neighbourhood. The set of FSAs define a cell space of ...
A block cellular automaton or partitioning cellular automaton is a special kind of cellular automaton in which the lattice of cells is divided into non-overlapping blocks (with different partitions at different time steps) and the transition rule is applied to a whole block at a time rather than a single cell.