Other [symbolic systems] rules

If only a single variable appears in the rule, then typically only nested behavior can be generated—though in an example like ℯ[x_][_]  ℯ[x[ℯ[ℯ][ℯ]][ℯ]] it can be quite complex. The left-hand side of each rule can consist of any expression; ℯ[ℯ[x_]][y_] and ℯ[ℯ][x_[y_]] are two possibilities. However, at least with small initial conditions it seems easier to achieve complex behavior with rules based on ℯ[x_][y_]. Note that rules with no explicit e's on the left-hand side always give trees with regular nested structures; x_[y_]  x[y][x[y]] (or x_  x[x] in Mathematica), for example, yields balanced binary trees.