Context of a solution

We distinguish between two kinds of solution, depending on their context :  A solution in a narrow context,  when  CA rule is constant and, a wide context solution, when CA rule varies. An isolated CA [rule=600] is a solution of the first kind. When parts of its rule are injured, it is driven out of its isolation,  entering a wider context . The outcome may vary. CA may expand, or it may die. It may also take up a stable oscillation, which is regarded here as a solution.

Three such solutions where depicted in a previous experiment when the rule was injured at t = 1. The present experiment explores what happens when the rule is injured at rising times. In the image below, when the rule is  injured at times 1 - 6 the CA maintains its structure (does not respond). Only at t  = 7   it is driven out  of its isolation, enters a short transitory phase after which it creates a new solution. When the rule is injured at t = 8, CA dies. Between t = 9-52 it does not respond. At t = 53 CA starts its new cycle, whose period is 46, and responds like at t = 7.

In the next experiment the CA responds to rule injury at t = 3.  Then comes  a brief period during which it does not respond { 4-11 }. Rule injury at t = 12 kills it. At t = 17 the CA starts expanding, then settles at the same solution like  that created at  t =3. Following a rule injury at t = 31 the CA creates a new solution. At t = 49 the cycle starts again.

Rule injury is induced here by the observer. Imagine that the same injuries were initiated by a CA. The three solutions depicted above are joint creations of the two CA. They are wide context solutions.  On its own,  CA[600] can never create these solutions since they were initiated by changing the rule. Part of the CA[600]  narrow context solution set is depicted in chapter 53

Transformation  invariance

A closer look at the non responding states reveals an interesting CA property.  Take the CA state  at t = 1 Despite interaction with three different rules, its subsequent  state remains the same. Transformation of this state was invariant under three different rules (mappings), rule 600, and its two injured sequels.  And so are  also other non responding  states.

nca=1 zygote -> effect[no 1000]; go109]; restoreparams;  putinstep [ If[j > mm =20, rul1[[21,2]] = 2; rul[[1]] = rul1];  go[100];  solutions: {a. color, rule-position, time} a017mm, a221mm..

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