# Wolfram's elementary automatons

In mathematics and computation theory there are a class of cellular automatons which are known as elementary automatons. This class of cellular automatons is restricted to the one dimensional grid (in the figures below the second dimension, ordinate (vertical) axis, is time) with cells either on or off. Another important simplification is that the actual state of the cell at given time, \( x_{i,t} \), depends only on the previous state of the same cell and the previous states of its immediate neighbors, i.e., on \( \{x_{i-1,t-1},x_{i,t-1},x_{i+1,t-1}\} \). Due to these restrictions and simplifications, generally speaking cellular automatons might evolve in the infinite dimensions, have infinite neighborhoods and have limitless number of possible cell states, these cellular automatons appear to be very simple, though as we show below they can replicate very complex and even chaotic behavior.