the interesting aspect of reversible CA's is that any "program" built with them that turns an input into an output also, as a side effect, produces an invertible program that can turn the output back into the input.
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here's the fastest known glider for the SRRCA, one for every axis aligned direction. there are over 90 different spaceships possible, which are able to travel at different angles and speeds.pic.twitter.com/CAIoZUQlFS
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90° rotators for 6-cycle gliders. each turn completes in 330 cyclespic.twitter.com/THbzDbzN14
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gliders can't be destroyed, and they can't be trapped (as that would violate reversibility); but they can get stuck at rigid obstacles for long periods of time, which could be used to halt gliders long enough to finish a program.
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gliders of same phase hitting each other just right can perform a horizontal -> vertical flip in 22 cycles.pic.twitter.com/MyHI1jQsAQ
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"electrons" can also solve mazes. ;-)pic.twitter.com/eKktyF4iiE
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apparently it was shown in 1977 that any irreversible d-dimensional cellular automaton rule can be turned into a reversible (d + 1)-dimensional rule. so many features of irreversible CA, such as ability to simulate Turing machines, can be extended to reversible CA.
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another ruleset for a reversible cellular automaton, the "billiard ball machine". while the rules are fairly simple, which is why i initially dismissed them as boring, one gets interesting behavior inside obstacle courses:pic.twitter.com/PMUVq4jvcy
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here for example is a (fairly useless) XOR circuit implemented in the BBM-CA.pic.twitter.com/XKUxfGTfGv
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found another reversible CA called "Double Rotation Rule" which is good for uh...pic.twitter.com/BogYgsMcoK
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I suspect it was you who came up with the linked rule and it's super interesting actually, it has inverse gliders from time to time and other things as well https://dmishin.blogspot.com/2013/11/the-single-rotation-rule-remarkably.html?showComment=1550606166625#c7690414334022566085 …pic.twitter.com/kMoYudNzV0
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