f[state[j, i], rule[#], max age] = f[state[j, i - 1], rule[#], state[j , i - k ]]

In the previous experiment the interaction of two self-impacting CA created a CA life cycle.   The state of CA-1  shaped the CA-2 structure, and  since CA-1 was periodic, CA-2 inherited the period.

In the present experiment  previous CA states shape the current CA structure. The first is an untreated cycling CA. Next to it is the same CA at time = 40. Its subsequent evolution depends on the state which shapes the current state at t = 40. Next to it is a CA whose evolution is shaped by the state at t = 33, or -7 which is relative to the current state. Next to it is a CA whose current state is shaped by the state at  t = 32. or -8.

The graph depicts cell count as a function of the previous state which interacts with the current state. Its period is 16.

Recollection

The CA  at t = 40 ( = now) remembers its previous experience,  which is stored in previous states,   and applies it for its current tasks. Suppose that its task is to maximize its future cell count, it will turn to states -8 or -24.  The 39 states are the CA memory, which  stores tasks and is decentralized.

CA repertory

The graph  depicts a CA repertory for maximizing cell count. There are many other. They depend on the interaction of a previous state with the current one. Each kind of interaction generates a different repertory.

The last images depict the same experiment with a non cycling CA.

Setup
prevdat = nowdat[[1]]; memorytime = 40; delmemory = *; ss = 0; ss = prevdat[[12]]; effect[1, 1, 20 - sa[[1]]+ ss];prevdat = nowdat[[1]]; memorytime = 40; delmemory = *; ss = 600; ss = prevdat[[12]]; effect[1, 1, 10 + sa[[1]] + ss];

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