An example originally popular in the earth and environmental sciences is so-called mathematical morphology, based on "dilation" of data consisting of 0's and 1's with a "structuring element" σ according to Sign[ListConvolve[ σ , data, 1, 0]] (as well as the dual operation of "erosion").

Cyclic tag systems [emulating tag systems] From a tag system which depends only on its first element, with rules given as in the note below, the following constructs a cyclic tag system emulating it: TS1ToCT[{n_, subs_}] := With[{k = Length[subs]}, Join[Map[v[Last[#], k] &, subs], Table[{}, {k(n - 1)}]]] u[i_, k_] := Table[If[j  i + 1, 1, 0], {j, k}] v[list_, k_] := Flatten[Map[u[#, k] &, list]] The initial condition for the tag system can be converted using v[list, k] .

Nested structure of attractors Associating with each sequence of length n (and k possible colors for each element) a number Sum[a[i] k -i , {i, n}] , the set of sequences that occur in the limit n  ∞ forms a Cantor set.

In the phyllotaxis process discussed in the main text one new element is produced at a time.

Given a sequence of length n , an approximation to h can be reconstructed using Max[MapIndexed[#1/First[#2] &, FoldList[Plus, First[list], Rest[list]]]] The fractional part of the result obtained is always an element of the Farey sequence Union[Flatten[Table[a/b, {b, n}, {a, 0, b}]]] (See also pages 892 , 932 and 1084 .)

The second-to-last case always has a black element at every third position, so exhibits a peak at the corresponding repetition frequency.

The third element of the rule is at first used only on some steps—but after step 50 it appears to be used somewhere in every step.

And I strongly suspect that even in many of the most basic everyday physical processes, every element of the underlying rule for the universe will be very extensively exercised.

The extraction of features by this kind of simple template matching appears to be a key element in human visual perception—as well as being common in technological image processing.

As a very simple idealization of biological evolution, one can consider a sequence of cellular automaton programs in which each successive program is obtained from the previous one by a random mutation that adds or modifies a single element.