# 7.3. Wolfram’s Experiment¶

In the early 1980s Stephen Wolfram published a series of papers presenting a systematic study of 1-D CAs. He identified four categories of behavior, each more interesting than the last.

In Wolfram’s experiments, the cells are arranged in a lattice which you might remember from Section 5.3 where each cell is connected to two neighbors. The lattice can be finite, infinite, or arranged in a ring.

The rules that determine how the system evolves in time are based on the notion of a “neighborhood”, which is the set of cells that determines the next state of a given cell. Wolfram’s experiments use a 3-cell neighborhood: the cell itself and its two neighbors.

In these experiments, the cells have two states, denoted as 0 and 1 or “off” and “on”. A rule can be summarized by a table that maps from the state of the neighborhood (a tuple of three states) to the next state of the center cell. The following table shows an example:

The first row shows the eight states a neighborhood can be in. The second row shows the state of the center cell during the next time step. As a concise encoding of this table, Wolfram suggested reading the bottom row as a binary number; because 00110010 in binary is 50 in decimal, Wolfram calls this CA “Rule 50”.