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Elementary Cellular Automata for Feynman Checkerboards/Group Theory

GROUPS:

Tony Smith has a 4-dim Feynman Checkerboard Model that is referenced in Wikipedia’s Feynman Checkerboard article. Tony relates the Clifford Algebra gradings of his model to the number of one bits in Elementary Cellular Automata. In http://vixra.org/pdf/1611.0030v2.pdf, I used the Cartan subalgebra of the group theory in Tony’s model to create this partitioning of the ECA rule space.

Rule Space Partitioning

ECA rules seem like switches when used for links in Tony’s Feynman Checkerboard model. Using ECA on links does fit with ECA being 1-dim and I can at least in part picture using ECA with a Feynman Checkerboard. Any thoughts on this rule space partitioning and on relating ECA rules to the Feynman Checkerboard and group theory would be welcome.

POSTED BY: John Gonsowski
Answer
1 year ago

Did you use Mathematica for this and can you share the code?

POSTED BY: Sam Carrettie
Answer
1 year ago

Mathematica wasn't used. I was forced into this particular rule space partitioning by Tony Smith's physics model. It would be nice to have a demonstration for partitioning of the rule space. I did quickly look to see what would have to change in Rodrigo Obando's partitioning for his to have the binary values be in ascending order (he was clustering based on class so he had a different order) and that kind of got me interested in different ways to do the partitioning beyond just the one that fits with Smith's physics.

POSTED BY: John Gonsowski
Answer
1 year ago

Group Abstract Group Abstract