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A special class of cellular automata are totalistic cellular automata. The state of each cell in a totalistic cellular automaton is represented by a number (usually an integer value drawn from a finite set), and the value of a cell at time t depends only on the sum of the values of the cells in its neighborhood (possibly including the cell ...
The Rule 110 cellular automaton (often called simply Rule 110) [a] is an elementary cellular automaton with interesting behavior on the boundary between stability and chaos. In this respect, it is similar to Conway's Game of Life .
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.
The rule for the automaton within each of these subsets is equivalent (except for a shift by half a cell per time step) to another elementary cellular automaton, Rule 102, in which the new state of each cell is the exclusive or of its old state and its right neighbor. That is, the behavior of Rule 90 is essentially the same as the behavior of ...
Initially, much of the cell-space, the universe of the cellular automaton, is "blank", consisting of cells in the ground state U. When given an input excitation from a neighboring ordinary- or special transmission state, the cell in the ground state becomes "sensitised", transitioning through a series of states before finally "resting" at a ...
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. Block cellular automata are useful ...
If we view the two states as Boolean values, this correspondence between ordinary and second-order automaton can be described simply: the state of a cell of the second-order automaton at time t + 1 is the exclusive or of its state at time t − 1 with the state that the ordinary cellular automaton rule would compute for it. [4]
The one-dimensional cyclic cellular automaton has been extensively studied by Robert Fisch, a student of Griffeath. [1] Starting from a random configuration with n = 3 or n = 4, this type of rule can produce a pattern which, when presented as a time-space diagram, shows growing triangles of values competing for larger regions of the grid.