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Converting isotropic life-like rules to Neumann rules

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Converting isotropic life-like rules to Neumann rules

Postby Naszvadi » January 21st, 2019, 3:57 am

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 reaction
x = 8, y = 16, rule = B2ae3anq/S
bo$o5$bo$o$o$bo5$o4bobo$bo3bo!


@RULE B2ae3anqNEUMANNED

@TABLE

n_states:4
neighborhood:vonNeumann
symmetries:permute

var 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 Moore
1,a,b,c,d,0
# two or more neighbours in Moore
2,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.)
3,0,0,0,0,3
3,a,b,c,d,0
0,3,3,a,b,2
0,3,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
# B2a
0,0,0,1,2,3

@COLORS

1 255 255 96
2 96  96  255
3 255 255 255


x = 21, y = 14, rule = B2ae3anqNEUMANNED
5.C.C3$2.C$3.C$C9.C.C$13.C2$13.C3$20.C2$20.C!
Naszvadi
 
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Re: Converting isotropic life-like rules to Neumann rules

Postby 77topaz » January 21st, 2019, 5:10 pm

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.
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Re: Converting isotropic life-like rules to Neumann rules

Postby Naszvadi » January 22nd, 2019, 4:07 am

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).
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Re: Converting isotropic life-like rules to Neumann rules

Postby dvgrn » January 22nd, 2019, 12:54 pm

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.
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