Representing an Integer with an Elementary Automaton

A positive integer can be represented using an elementary cellular automaton by the vector consisting of the rule, the initialization, and the step. Of course, there is the trivial representation with zero steps, but if the number is large, its vector will have a large norm. There may be many equivalent representations; these equivalents can be ordered by their norms. Equivalents for the same number are shown as points and the one currently selected is marked by a line connecting it to the origin. The corresponding automaton evolution is shown as an array with the base-two representation of the target.