The rules for the multiway system can then be given for example as {"AAB"  "BB", "BA"  "ABB"} The evolution of the system is given by the functions MWStep[rule_List, slist_List] := Union[Flatten[ Map[Function[s, Map[MWStep1[#, s] &, rule]], slist]]] MWStep1[p_String  q_String, s_String] := Map[StringReplacePart[s, q, #] &, StringPosition[s, p]] MWEvolveList[rule_, init_List, t_Integer] := NestList[MWStep[rule, #] &, init, t] An alternative approach uses lists instead of strings, and in effect works by tracing the internal steps that Mathematica goes through in trying out possible matchings.

Larger objects normally come to the top (as with mixed nuts, popcorn or pebbles and sand), essentially because the smaller ones more easily fall through interstices.

In organisms with a total of just a few thousand cells, the final position and type of every cell seems to be determined directly by the genetic program of the organism; most likely what happens is that each cell division leads to some modification in genetic material, perhaps through rules like those in a multiway system.

So this suggests that somehow the complexity we see must arise from some straightforward and general mechanism—and not, for example, from a mechanism that relies on elaborate refinement through a long process of biological evolution.

But we seem to be forced to progress through time in a very specific way.

But if the underlying rules for the network preserve planarity then each of these pieces of non-planarity must on their own be persistent—and can in a sense only disappear through processes like annihilating with each other.

To define the spacetime Ricci tensor, one considers—as on page 516 —a sequence of spacelike slices through this

But in a sense a structure that corresponds to a particle will normally not fit through this path.

The idea is just to form an encrypting sequence by repeatedly cycling through the elements in the key.

But when the line is black, it lets lines coming from the left through.