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Posted by Jesse Nochella on 01-13-2005 05:06 AM:

A thought provoking picture of rule 110

Attached is a picture of what happens when you apply cellular automaton rule 110 over and over again, starting with blank inital conditions, and with one cell cycling a forced color in form of the repeating pattern "1, 0, 1, 1, 0, 1, 0, 0", for fifteen thousand steps. Its rather interesting.

Posted by Tommaso Bolognesi on 01-19-2005 10:24 AM:

Hi Jesse,

very nice picture. Once can scroll the window at constant speed and see a kind on animation of the interactions that take place.
Which one is the column that you have perturbed with your cyclic sequence?
Did you try with simpler (shorter) cycles,
maybe (0,1) ?

__________________
========================================================================
Tommaso Bolognesi
Formal Methods && Tools Lab.
CNR - ISTI - Pisa - Italy
e-mail: t.bolognesi@iei.pi.cnr.it
web: http://matrix.iei.pi.cnr.it/FMT/

Posted by Jesse Nochella on 01-22-2005 03:09 AM:

I did try others, some of what I've written on these kinds of pertubations have is in my post on causal precursors here, particularly in the post titled "A phenomenon with uncanny similarity to entropy increase".

One thing to note about this particular graphic is that I am encountering a abberation in rendering where there is 1 too many pixels across, and so an extra column in the middle ( anyone knowing of how to fix this I would greatly appriciate help with).

The cell that is being perturbed is the rightmost in the picture. What happens is from a blank inital condition, consisting of all zeros, the first cell of the sequence is put in. Rule 110 grows only to the left, so that't why its the rightmost cell in this case. If the rule grew in both directions, like in a totalistic rule, the pertubation would be in the center cell.

most cases of these as with {0,1} behave in complex ways for short time and then terminate, but some, as in condition 5 and condition 180 persist for very long periods of time. I have an archive of the first 1000 of these conditions that I will post shortly.

I chose to show condition 180 because it was especially elegant and persists for an extremely long time, and still I am not entirely sure whether it repeats or not.

But I have never seen a repeating sequence that yields obvious complex behavior, and so my conjecture about this is that so far as repeating sequences go, every single case exhibits repetition. This is analogous to initial conditions of finite repetition period.

I think it's quite a powerful concept - for it implies that as far as a model for our universe goes, we need not an infinite recursion of processes to explain phenomena. But there's also some more applicable features that can be used as tools for understanding.

One example is the notion that given control over this live input, we know that any kind of repeating sequence will eventually reduce all of the cells it influences to a simple state that corresponds to a computation of less sophistication than us. But alongside of this is another important observation - that even though any sequence will ultimately work, what happens throughout and in the end can vary immensely depending on the repeating sequence we use.

It's just amazing how properties that are so obvious in this simple graphical representation turn up having all these parallels to our actual world. Who's to say they don't correspond to the same fundamental phenomenon?

I don't know, but the pictures make you think. Thats why I put them up. These pictures are simple enough to build a great intuition.