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HPSSBB (Highest period supporting specific bounding boxes) (3-state OT edition)
Posted: February 25th, 2025, 2:19 pm
by unname4798
This is similar to
viewtopic.php?f=11&t=6879, but only for 3-state OTCA.
1x1:
Code:
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#R Oneby1
A!
@RULE Oneby1
@TABLE
n_states:3
neighborhood:Moore
symmetries:permute
1,0,0,0,0,0,0,0,0,2
2,0,0,0,0,0,0,0,0,1
1x2:
Code:
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#R Oneby2
2A!
@RULE Oneby2
@TABLE
n_states:3
neighborhood:Moore
symmetries:permute
1,1,0,0,0,0,0,0,0,2
2,2,0,0,0,0,0,0,0,1
Re: HPSSBB (Highest period supporting specific bounding boxes) (3-state OT edition)
Posted: February 26th, 2025, 8:37 am
by confocaloid
I think the idea is interesting and may deserve investigation. See also related discussion, although that one isn't restricted to outer-totalistic cellular automata:
viewtopic.php?f=11&t=6047 Upper limit for oscillator period with N cells in envelope box)
It may be interesting to see how far one can go without RuleLoader. Here is a p71428 oscillator with bounding box 10-by-10:
Code:
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x = 10, y = 10, rule = 2345/45678/3
5A$A.4A$2A2.3A$2A2.4A$6A.2A$7A.2A$A3B2.A2.A$A.5A2.A$.A.2A.3A$2.6A!
#C [[ GRID ]]
And here is a p107334 oscillator with bounding box 9-by-9:
Code:
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x = 9, y = 9, rule = B23678/S3478Investigator
9O$O.2A4.O$O2A.A.A.O$O7AO$O4A3.O$O.A.A.2AO$O2.3A2.O$O6.AO$9O!
#C [[ GRID ]]
Note that in each case, there are only three distinct cellstates (the background zero + two nonzero cellstates) appearing through the entire evolution of the oscillator, and in each case, the rules are outer-totalistic, so it should count as ontopic here. I'm not sure which of two approaches is going to lead to highest possible periods. (Of course both will be beaten by arbitrary RuleLoader-supported files with "n_states:3 / symmetries:permute".)