plaid diagram

Figure 1.27: Excluded words are responsible for the plaid diagram's woven texture.

The same information shows up in the plaid diagram. A plaid diagram is obtained by first selecting an origin for a configuration. The sequence of cell states, assuming they are represented by integers modulo $k$, the number of states, is then regarded as a $k$nary number lying in the interval 0 - 1, which is considered to be the $x$-coordinate of a point. The same process is applied to the portion of the configuration lying to the left of the origin, except that it is read backwards from the origin, and used as the $y$-coordinate of a point.

The plaid diagram is made by tracing the trajectories of several initial configurations for a number of generations. Garden of Eden configurations will have a low density because they can only be found at the beginning of a trajectory; their absence will show up as blank strips. Recall that any sequence which begins or ends with an excluded string is also excluded, which gives width to the strips. .