Saturday, August 01, 2020

[bdndzgyq] It's cellular automata all the way down

Design a cellular automaton in which most behavior seems to be governed by simple rules, but some things appear random or more complicated.  Those more complicated things, as well as all the simpler behavior, are actually all governed by another cellular automaton at a "lower" level.  Then, that lower cellular automaton in turn has even lower cellular automata that control it, and so on infinitely all the way down.

Inspired by real life, with particles composed of smaller particles.

How could such an infinite-regress cellular automata be simulated?  We probably have to cheat somewhere, making approximations, for example, substituting a random number generator for low-level randomness.

One way to depict a simple form of infinite regress would be to use or abuse a Conway's Game of Life unit cell, for example the OTCA or 0E0P metacells.  Zooming in substitutes unit cells for monolithic cells.  (The cheat here is that Life is fully determined by its rules at one level and does not need the lower cellular automaton, so we can put one in or take it out whenever we want.)

Incidentally, the above construction of using unit cells to similar infinite regress in Conway's Game of Life demonstrates local hidden variables.  Bell's Inequality showed that what we yet don't know about our universe (perhaps levels of cellular automata too small for us to see) cannot be modeled with local hidden variables.  Design a lower cellular automata to have global effects, perhaps a yielding what looks at the upper level to be a cellular-automata version of quantum mechanics's spooky action at a distance.

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