Converting isotropic life-like rules to Neumann rules

For discussion of other cellular automata.

Converting isotropic life-like rules to Neumann rules

For rule B2ae3anq/S , there is a corresponding 4-state Neumann rule. It is shrunk from 6 states, further optimizations might be possible.

Original reactions:
`#C Three gliders and a one-time turner, pulling reactionx = 8, y = 16, rule = B2ae3anq/Sbo\$o5\$bo\$o\$o\$bo5\$o4bobo\$bo3bo!`

`@RULE B2ae3anqNEUMANNED@TABLEn_states:4neighborhood:vonNeumannsymmetries:permutevar a={0,1,2,3}var b={0,1,2,3}var c={0,1,2,3}var d={0,1,2,3}#    +-+#    |b|#  +-+-+-+#  |o|1|b|#+-+-+-+-+-+#|o|2|b|0|b| === B2a#+-+-+-+-+-+#  |b|0|b|#  +-+-+-+#    |b|#    +-+##    +-+#    |b|#  +-+-+-+#  |o|1|b|#+-+-+-+-+-+#|o|2|b|1|o| === B3q#+-+-+-+-+-+#  |b|0|b|#  +-+-+-+#    |b|#    +-+##    +-+#    |b|#  +-+-+-+#  |o|2|o|#+-+-+-+-+-+#|b|1|b|1|b| === B2e#+-+-+-+-+-+#  |b|0|b|#  +-+-+-+#    |b|#    +-+##    +-+#    |o|#  +-+-+-+#  |o|2|b|#+-+-+-+-+-+#|b|1|b|1|o| === B3n#+-+-+-+-+-+#  |b|0|b|#  +-+-+-+#    |b|#    +-+##    +-+#    |o|#  +-+-+-+#  |o|2|o|#+-+-+-+-+-+#|b|1|b|1|b| === B3a !!!!! 2 === 3 in this particular case!#+-+-+-+-+-+#  |b|0|b|#  +-+-+-+#    |b|#    +-+## one neighbour in Moore1,a,b,c,d,0# two or more neighbours in Moore2,a,b,c,d,0# alive cell in Moore is assigned to state 3# (state 0 has multiple rules like background, dead cell, empty neighbours etc.)3,0,0,0,0,33,a,b,c,d,00,3,3,a,b,20,3,a,b,c,1# B2e + B3n <- (0,1,2,1), and isomer B3q <- (0,1,1,2)# B3a <- (0,1,3,1)0,0,1,1,2,3# B2a0,0,0,1,2,3@COLORS1 255 255 962 96  96  2553 255 255 255`

`x = 21, y = 14, rule = B2ae3anqNEUMANNED5.C.C3\$2.C\$3.C\$C9.C.C\$13.C2\$13.C3\$20.C2\$20.C!`

Posts: 349
Joined: May 7th, 2016, 8:53 am

Re: Converting isotropic life-like rules to Neumann rules

Hmm... this is similar to the mechanism the 0E0P metacell uses, right? That also simulates Moore rules as multi-state von Neumann rules with a slower timestep.

77topaz

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Joined: January 12th, 2018, 9:19 pm

Re: Converting isotropic life-like rules to Neumann rules

77topaz wrote:Hmm... this is similar to the mechanism the 0E0P metacell uses, right? That also simulates Moore rules as multi-state von Neumann rules with a slower timestep.

Allegedly 0E0P uses a similar method in order to simulate Moore neighbourhood, however I haven't checked it yet.

Also a translation table for the isotropic 2-state rules would be handy, planned to create them focusing on particular optimizations on used number of states in destination cellspace (Neumann).

Posts: 349
Joined: May 7th, 2016, 8:53 am

Re: Converting isotropic life-like rules to Neumann rules

Naszvadi wrote:Allegedly 0E0P uses a similar method in order to simulate Moore neighbourhood, however I haven't checked it yet.

Also a translation table for the isotropic 2-state rules would be handy, planned to create them focusing on particular optimizations on used number of states in destination cellspace (Neumann).

Here's the script to look at if you want to see how the 0E0P isomorphism works. It uses eight states and a restricted neighborhood.

Apparently the mapping was found via an exhaustive search, and therefore there is no seven-state solution that works for all possible non-totalistic rules under the same restrictions. No doubt some rules will need less than eight states, but seven won't be enough for certain rules. I don't know what happens if you remove the requirement that cells die after one tick.

dvgrn
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