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Published on Aug 13, 2014
This is an example of a cellular automata rule in 3 dimensions, which permits a glider to be constructed which moves with (asymptotically) any velocity along the X,Y,and Z axis simultaneously. Thus is had the property of motion in (asymptotically) any direction and at (asymptotically) any velocity.
As the width, height, or length dimensions of the glider are increased, it will propagate more slowly along that axis. As will be shown below, the speed of propagation along an axis is inversely proportional to the length of the glider in that axis.
This is interesting because it shows that with a simple local rule on a cartesian lattice, you can obtain motion which is rotationally isotropic. This has implications for discrete physics models of subatomic physics. It has been observed that atoms, and the subatomic particles such as electrons, protons, and neutrons which make them up, appear to be able to move in any direction in space, with apparently arbitrary velocity. So any model we make using cellular automata should be able to support isotropic motion which does not, at any but perhaps the smallest scale, have a preferred axis of motion. The rule described here serves as a sort of existence-proof that such angular isotropic motion is obtainable from a local cellular automata rule which has a highly local cartesian neighborhood.
The rule is implemented within Fredkin's SALT model framework for a conservative reversible 3D cellular automata.