Converting isotropic life-like rules to Neumann rules

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Naszvadi
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Converting isotropic life-like rules to Neumann rules

Post by 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:

Code: Select all

#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!

Code: Select all

@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

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x = 21, y = 14, rule = B2ae3anqNEUMANNED
5.C.C3$2.C$3.C$C9.C.C$13.C2$13.C3$20.C2$20.C!

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77topaz
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Joined: January 12th, 2018, 9:19 pm

Re: Converting isotropic life-like rules to Neumann rules

Post by 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.

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

Post by 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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dvgrn
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Re: Converting isotropic life-like rules to Neumann rules

Post by 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.

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

Post by Naszvadi » March 21st, 2020, 8:04 am

"Gun!"
"GUN!"
"Gun left!"

Original by: https://www.youtube.com/watch?v=aa2agiADM04&t=9

Code: Select all

x = 191, y = 117, rule = B2ae3anq/S
102bobo$101bo3bo7$102b2o3$73bo13bo7bo14bo7bo$74bo11bo7bo7b2o7bo7bo$86b
o7bo7b2o7bo7bo$74bo12bo7bo14bo7bo$73bo2$102b2o7$100bo3bo72b2o$22bobo
76bobo72bo2bo$21bo3bo103b2o$128bo2bo5$177b2o$176bo2bo$129b2o$22b2o28bo
75bo2bo$9bo7bo10bo7bo14bo$8bo7bo12bo7bo$8bo7bo12bo7bo13bo66bo$9bo7bo
10bo7bo15bo64bo23bo$22b2o103bo4bo9bo23bo10b2o$117bo9bo4bo32bo10bo2bo9b
o$118bo23bo28bo12bo5bo$141bo23bo5bo12bo$166bo9bo2bo10bo$177b2o10bo$
128bo2bo$129b2o2$20bo3bo$21bobo2$176bo2bo$177b2o$128bo2bo$129b2o5$176b
o2bo$177b2o8$129bobo$128bo3bo$177bobo$176bo3bo19$22bobo$21bo3bo5$22b2o
3$3bo38bo$2bobo36bobo$bobo9bo7bo2bo7bo9bobo$o11bo7bo4bo7bo11bo$o11bo7b
o4bo7bo11bo$bobo9bo7bo2bo7bo9bobo$2bobo36bobo$3bo38bo3$22b2o5$20bo3bo$
21bobo!
And a higher ship with greater period with a pre-gun configuration, a period doubler and converter.

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