Re: Permutation City

From: Anders Sandberg (
Date: Wed Apr 19 2000 - 17:35:08 MDT

mjg223 <> writes:

> On Wed, 19 Apr 2000, Anders Sandberg wrote:
> > I have spent this weekend attempting to evolve causality in a
> > cellular automaton (I wanted to find a 2D automaton rule that
> > generated patterns corresponding to the space-time diagrams of a 1D
> > automaton), and it was definitely tricky.
> Interesting stuff. A rule like: 'fire if my right-hand neighbor is firing'
> would generate leftwards trajectories. You could elaborate on that to get
> traces to bounce off each other is you added a second class of firing
> mode. Are you looking for something deeper than that - what's the target
> you're trying to fit? Are you just doing thresholding on local neighbors
> or are you using a more sophisticated class of 1D automation?

The origin of the experiment is a cosmological idea I have been
playing around with: the entire 4-D history of the universe is a
stable state of a 4-D cellular automaton. If this hypothetical CA is
started with a random state, then it will converge to an allowable
history of the universe.

My experiment was far simpler, I used a 2D automaton with binary
states and the Moore neighbourhood and a 2^9 bit rule denoting the
result of every possible local state (this was the genes I ran the GA
on). After running the automaton for a few steps, I calculated fitness
from the final state. At first I tried to make the fitness function
depend on how well the pattern fitted a predetermined 1-D rule, but
right now I'm just contenting myself trying to get a causal evolution
(i.e. a one-to-one mapping of states in the previous row to the
next). So far I have not yet succeeded.

As I see it, the interesting question is if you can get the 2D
automaton to evolve a consistent state from a random state. It would
also incorporate the possibility of "synchronicity" and nonlocal
interactions, as two separated patterns in the 1D world could have
been affected by precursor states at early steps in the 2D world.

Anders Sandberg                                      Towards Ascension!                  
GCS/M/S/O d++ -p+ c++++ !l u+ e++ m++ s+/+ n--- h+/* f+ g+ w++ t+ r+ !y

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