Langton's Ant Challenge

For discussion of other cellular automata.
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creeperman7002
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Langton's Ant Challenge

Post by creeperman7002 » December 30th, 2021, 4:14 pm

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:
Attachments
Langtons-ant-resolved.zip
(5.59 MiB) Downloaded 30 times
B2n3-jn/S1c23-y 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.
viewtopic.php?f=11&t=4856

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