2.9 Connectedness

All the rules we have seen so far maintain connectedness. It is, however, straightforward to set up rules that do not. An obvious example is:

At step n, there are 2ⁿ⁺¹ components altogether, with the largest component having n + 1 relations.

Rules that are themselves connected can produce disconnected results:

Rules whose left-hand sides are connected in a sense operate locally on hypergraphs. But rules with disconnected left-hand sides (such as {{x},{y}}→{{x,y}}) can operate non-locally and in effect knit together elements from anywhere—though such a process is almost inevitably rife with ambiguity.