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The top row shows the effect of inserting a single extra black cell into various backgrounds.
By inserting k = 6 Ceiling[Length[subs]/6] in the definition of TS1ToCT from page 1113 one can construct a cyclic tag system of this kind to emulate any one-element-dependence tag system.
At an idealized level one might imagine trying to do this by inserting into the system some kind of paddle which would experience force as a result of impacts from particles.
EvenQ] := Partition[ Fold[Insert[#1, #2, Random[Integer, Length[#1]] + 1] &, {}, Floor[Range[1, n + 2/3, 1/3]]], 2]
Networks obtained in this way are usually connected, but will almost always contain self-loops and multiple edges.
For Sin[a x] + Sin[b x] a more complicated sequence of substitution rules yields the analogous sequence in which -1/2 is inserted in each Floor .
And is it perhaps all somehow just a reflection of randomness that was inserted in the initial conditions?
Addition modulo n can be handled by inserting Modulus n in NullSpace in the previous note.
In both cases, the new nodes are inserted in the "above" connection from each node.
One, illustrated in picture (c) at the bottom of the facing page , is to insert at the beginning of each number a specification of how many digits the number contains.
And in the second mechanism for randomness discussed at the beginning of this chapter , no explicit randomness is inserted during the evolution of a system.