After discovering several LA rules that take more than a billion steps to settle into predictable behavior, I decided on making this thread inspired by this one.
The challenge is to discover a rule that has 12 colors or less and breaks the following record:
LLLLLLLLRL (2,130,000,000 steps)
A rule of interest here is LLLLLLLLRRLR, which I have observed to produce a highway on a limited canvas but remains chaotic after 10 billion steps on an infinite grid.
Here are some things to do along with the challenge stated above:
1. Run LRL to 1 trillion steps or more. Does the rule become predictable by then?
2. Discover a rule that takes 10 billion steps or more to settle into predictable behavior.
3. Prove that a certain rule remains chaotic forever, if possible.
4. Provide an explanation as to why LLLRR stays near the origin and rarely ventures out.
Sorry if this thread seems like a copy of the turmite thread.
Here's a collection of rules known to be predictable after some time:
Langton's Ant Challenge
 creeperman7002
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 Joined: December 4th, 2018, 11:52 pm
Langton's Ant Challenge
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B2n3jn/S1c23y is an interesting rule. It has a replicator, a fake glider, an OMOS and SMOS, a wide variety of oscillators, and some signals. Also this rule is omniperiodic.
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viewtopic.php?f=11&t=4856