Registered: Feb 2004
Posts: 172

The result of an iteration of rule 30 (or any of the elementary rules) may be interpreted in the following way:

Each cell is either black or white.
Black means the algorithm represented by that cell is running (non terminating). White means it terminated.

If at a particular step any of the cells become black then that means the algorithm is running again.

Each cell viewed as representing the runtime state of a simple algorithm affords us the ability to view interaction of algorithms (how they affect each other).

Other variations on the theme include viewing a black cell as representing a different algorithm which does not terminate. The white cells would be algorithms which do terminate. Whatever type of algorithm is in the "cell" is variable (it could be a terminating kind or a non-terminating kind). The first theme above would be more "static." The algorithm in the cell does not change.

Anything thoughts on this perspective? I am interested in developing this a little bit more.

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Registered: Mar 2004
Posts: 19

To study run-times and interactions, one automatically has to treat the CA in question as an object that evolves over time. So one has to follow a "path" through the CA, i feel, and in an infinitely run CA there are infinite paths, so your choice of "paths" is arbitrary, as well as choise of path interactions. Not that i find this to be a drawback, it could be very informative...

This is related to your other post on the Integers, i suppose. one can study relationships between successive numbers, or just the odds, or evens, or every third, fourth, fifth,,,I guess "path" relationships between the integers could be viewed as arbitrary too. Still not a drawback.

Last edited by Jason Wesley Ellis on 12-22-2005 at 04:34 PM

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