wildmyron wrote:A for awesome wrote:If a p3 oscillator can be found (easier said than done, perhaps), Wire-/1V would be omniperiodic, becoming perhaps the simplest known omniperiodic rule:
p3
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x = 6, y = 6, rule = Wire-_1V
.B.B$.2BA2B$B3AB$.B3AB$2BA2B$2.B.B!
Now that Wire-/1V is known to be omniperiodic, it occurs to me just now that two even simpler rules support everything I posted before, plus a simpler p3 consisting of 4 active cells in a straight line:
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@RULE Wire-1_1V
@TABLE
n_states:3
neighborhood:vonNeumann
symmetries:permute
var a={0,1,2}
var b=a
var c=a
var d=a
var e={0,2}
var f=e
var g=e
var h={1,2}
h,1,e,f,g,1
1,a,b,c,d,2
@COLORS
1 128 128 255
2 0 255 0
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@RULE Wire-13_13V
@TABLE
n_states:3
neighborhood:vonNeumann
symmetries:permute
var a={0,1,2}
var b=a
var c=a
var d=a
var e={0,2}
var f=e
var g=e
a,1,e,f,g,1
a,1,1,1,e,1
1,a,b,c,d,2
@COLORS
1 128 128 255
2 0 255 0
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x = 29, y = 11, rule = Wire-1_1V
11.B$11.B3.B.B.B.B.B.B$B2.B7.B3.A13B$3.A7.A4.B.B.B.B.B.B.B$11.B14.2B$
25.2B$26.2B$25.2B$26.2B$25.2B$26.B$4A!
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x = 29, y = 11, rule = Wire-13_13V
11.B$11.B3.B.B.B.B.B.B$B2.B7.B3.A13B$3.A7.A4.B.B.B.B.B.B.B$11.B14.B$
25.2B$26.2B$25.2B$26.2B$25.2B$26.B$4A!
The first one is totalistic in the 4-cell VN neighborhood; the second is simply the wire version of the 4-cell VN XOR automaton. While Wire-1/1V is identical to Wire-/1V for starting patterns where all state-1 cells have the same parity, meaning that whatever circuitry in one should work in the other, the XOR automaton should behave somewhat differently due to B3, but retains its omniperiodicity (and could possibly even be computationally universal, making it perhaps the simplest universal automaton, as it is arguably simpler even than W110). My suspicion is that Wire-1/1V is universal but Wire-13/13V isn't, but that's nothing more than just a suspicion.
DISCLAIMER: Both rule tables and patterns contained within this post are entirely untested. I'm also really busy at the moment, so I may not be able to fix or even respond to anything for a while.