[Causal precursors in k=3 r=1] - A New Kind of Science: The NKS Forum

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Causal precursors in k=3 r=1

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Posted by: Jesse Nochella

After searching through about 15000 rules in k=3 r=1, I found 10 rules that I think might be causal precursors. They are:

{3360560874578, 6170234970207, 4366619420758, 3042853167429, 1640917018310, 6562810245337, 3522605405545, 2768943931613, 257974532413, 1987008035144}

Some of these I am sure qualify, like rule 3042853167429. Others I am not so sure about. But it's my guess that at least most of these rules do indeed qualify.

A causal precursor is a rule where unbounded universal behavior for sure interacts with unbounded class 3 behavior in absolutely any way for an infinite amount of time. I have an older thread that introduces them and has some of what I think about them on the forum here.

The basic idea is that for the rules whose output never repeats, a universal system of computation can use that output as a sort of perturbation to correspond to a computation of infinite variety that goes on forever. It's almost as if the universal part is trying to figure out what it's getting from the class 3 output, but it can never do it fast enough, so there's always something to do and the load keeps getting bigger.

All this happens in a completely deterministic way, and in the case of the rules above from a single black initial cell.

I suppose the computations inside would have occurrence probabilities that correspond to the strings of perturbation that generate them. I think it is an interesting course of study and it would be exciting to discover more rules that exhibit behavior of this kind. The ways that such behavior is formed I think has real significance; anyone with more rules, show them here if you like.

I should be looking for and finding more in k=3 r=1 soon. It would be interesting to discover how it happens in other systems. The simplicity alone of these rules seems to show that there is much for them to offer.


Posted by: Jesse Nochella

Here's an archive of 1800 steps each of the first half of the rules mentioned above.


Posted by: Jesse Nochella

Here's the second half.




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