At first it was not clear what idealizations to make, but by the late 1980s—especially through the work of David Deutsch —the concept had emerged that a quantum computer should be described in terms of a network of basic quantum gates.

In enumerating recursive functions it is convenient to use symbolic definitions for composition and primitive recursion c[g_, h___] = Apply[g, Through[{h}[##]]] & r[g_, h_] = If[#1  0, g[##2], h[#0[#1 - 1, ##2], #1 - 1, ##2]] & where the more efficient unwound form is r[g_,h_] = Fold[Function[{u, v}, h[u, v, ##2]], g[##2], Range[0, #1 - 1]] & And in terms of these, for example, plus = r[p[1], s] .

The geometrical pattern was presumably made by first constructing 48 regularly spaced spokes by repeated angle bisection, as in the first picture below, then drawing semicircles centered at the end of each spoke, and finally adding concentric circles through the intersection points.

The pictures show typical configurations generated after 1000 steps from various initial densities, as well as slices through their evolution.

But it was not clear how to extend the formalism say to a problem like propagation of light through a crystal.