Question from rookie

[shouldsee]

This k=5 neighbor don't fit into birth/survival notation that nicely, and we can easily find a different k=5 neighborhood on a pentagonal lattice. k=5 neighborhood is not uniquely defined, but this k=5 can be viewed as k=4 with extra symmetry.

So how does the rule work in the k5 neighborhood anyway? Tell me that and I can (hopefully) get a ruletable prepared.

The transition of central cell is determined by the number of 0-states 1-states and 2-states in the modified von Neumann neighborhood, where when counting neighbors, the central cell is a neighbor itself.

an exemplar k=4 rule table is as follows

Code: Select all

@RULE v3k4_000200121021212V



@TABLE
n_states:3
neighborhood:vonNeumann
symmetries:permute

var a={1}
var b={2}

var d={0}

var j={0,1,2}



j,0,0,0,0,0
j,0,0,0,1,0
j,0,0,1,1,0
j,0,1,1,1,2
j,1,1,1,1,0
j,2,0,0,0,0
j,2,1,0,0,1
j,2,1,1,0,2
j,2,1,1,1,1
j,2,2,0,0,0
j,2,2,1,0,2
j,2,2,1,1,1
j,2,2,2,0,2
j,2,2,2,1,1
j,2,2,2,2,2


@COLORS

0 0 0 0
1 0 155 155
2 200 200 0
3 200 0 200

we want k=5 rule table for 010222022022220021110.
if we can have another option for 'symmetry' that is 'homogeneous' then this would be lot easier.

[BlinkerSpawn]

I'm pretty sure this is wrong because we've got some strong B1 stuff going on here:

Code: Select all

@RULE k5_something_or_other
@TABLE
n_states:3
neighborhood:vonNeumann
symmetries:permute

000000
000011
100001
000110
100010
001112
100112
011112
101112
111112
000020
200000
000122
100022
200012
001122
100122
200112
011120
101120
201110
111122
211112
000222
200022
001222
100222
200122
011222
101222
201122
111220
211120
002220
200220
012222
102222
201222
112221
211221
022221
202221
122221
212221
222220

@COLORS

0 0 0 0
1 0 155 155
2 200 200 0

[FlameandFury]

Though the ruletable may be incorrect, there are still interesting spaceships and tagalongs:

Code: Select all

x = 11, y = 16, rule = k5_something_or_other
.2B.2B.2B$A.B2.B$A.B2.B$.2B.2B.B.2B$10.B$10.B$4.2B.B.2B$3.A.B$3.A.B$
4.2B.2B$7.A2B$7.A.B$4.2B2.2B$3.A.B$3.A.B$4.2B!

EDIT: A puffer

Code: Select all

x = 6, y = 4, rule = k5_something_or_other
.2B$A.B.2B$A.B.B$.2B!

EDIT 2: Wow.

Code: Select all

x = 9, y = 20, rule = k5_something_or_other
.2B$A.B$A.B$.2B.2B$4.A2B$4.A.B$.2B2.2B.B$A.B$A.B$.2B4$.2B$A.B$A.B$2.B
$A.B$A.B.B$.2B!

[shouldsee]

I have inverted the sequence to obtain this, which till looks suspicious.

Code: Select all

@RULE v3k5_011020022220220222010

@TABLE
n_states:3
neighborhood:vonNeumann
symmetries:rotate4reflect

000000

000011
100001

000111
100011

001111
100111

011112
101112

111110



000020
200000

000122
100022
200012

001122
100122
200112

011122
101122
201112

111122
211112



000220
200020

001222
100222
200122

011222
101222
201122

111220
211120




002222
200222

012222
102222
201222

112222
211222





022220
202220

122221
212221



222220




@COLORS

0 0 0 0
1 0 155 155
2 200 200 0