This Demonstration is a simple tool to browse the one-dimensional cellular automaton rules (0-255). It also includes a variation of the standard rules of automaton cells on a background. The length of the space is constrained by the "size" parameter and cells are absorbed at the ends. Controls and graphs let you explore convergence properties. A balance parameter forms the initial row using zeros on the left and ones on the right, more or less on each side as the slider dictates.
The list graphs show the convergence of the sequence in two ways. The top graph, "average value" is simply the average of 0 and 1 values along a row. The second graph takes each row and tests for equality cell by cell with the initial row before averaging. Also, as the caption says, the rules include absorption at the ends of the space. At either end a zero background is applied and cells evolving past the endpoints are deleted at each step.