Inverse of "Coagulations" rule (B478/S234678)

[Paul Tooke]

Calcyman wrote:

I haven't tested it, but I think that the following should work

I tested this on the p28 oscillator and Oscar claimed it was p5. I think that there's a typo in the table: it has "301033" and "303012", which is asymmetric. Replacing 303012 by 303013 (which I believe is the correct rule) fixed things. Well, at least Oscar now claims that the p28 is p28!

Here's the modified table:

Code: Select all

n_states:4
neighborhood:vonNeumann
symmetries:none

# Modified Gray code representation of states:
#
# 0 = ...
# 1 = .#.
# 2 = ###
# 3 = #.#


100000
100010
100021
100031
101000
101011
101022
101031
102001
102012
102021
102033
103001
103011
103023
103031

200001
200012
200023
200032
201002
201012
201022
201033
202003
202012
202021
202032
203002
203013
203022
203032

300000
300010
300023
300031
301000
301012
301023
301033
302003
302013
302022
302032
303001
303013
303022
303033

[Paul Tooke]

Here is an alternative rule table for the orthogonal width 3 symmetric 1D CA which combines ideas from ebcubes table (show cell history) with calcymans (include the background state).

Code: Select all

n_states:4
neighborhood:Moore
symmetries:none

# Modified Gray code representation of states:
#
# 0 = ...
# 1 = .#.
# 2 = ###
# 3 = #.#

0100000000
0100000010
0100000021
0100000031
0110000000
0110000011
0110000022
0110000031
0120000001
0120000012
0120000021
0120000033
0130000001
0130000011
0130000023
0130000031
    
0200000001
0200000012
0200000023
0200000032
0210000002
0210000012
0210000022
0210000033
0220000003
0220000012
0220000021
0220000032
0230000002
0230000013
0230000022
0230000032
    
0300000000
0300000010
0300000023
0300000031
0310000000
0310000012
0310000023
0310000033
0320000003
0320000013
0320000022
0320000032
0330000001
0330000013
0330000022
0330000033

Here is the p28 oscillator to try it out on:

Code: Select all

x = 24, y = 1, rule = 1D
ACBCB2A3BAB2CBA2B2AB2CA!

Here is a similar table for the 4 state 1D-CA emulated by some of the diagonally symmetric oscillators:

Code: Select all

n_states:5
neighborhood:Moore
symmetries:none

# 1-D CA emulated diagonally in B478/S23468
#
# Representation of states:
#
# 0 = background
# 1 = #.. 2 = ##. 3 = #.# 4 = ###
#     .??     #??     .??     #??
#     .??     .??     #??     #??

#Eastern edge: treat background as state 1
0100000011
0100000021
0100000031
0100000041
0200000012
0200000022
0200000032
0200000044
0300000011
0300000024
0300000033
0300000044
0400000014
0400000023
0400000034
0400000043

#Western edge: treat background as state 1
0110000001
0120000001
0130000001
0140000002
0210000002
0220000002
0230000002
0240000001
0310000001
0320000002
0330000004
0340000003
0410000004
0420000003
0430000003
0440000004

#The remainder are unkludged
0110000011
0110000021
0110000031
0110000041
0120000011
0120000022
0120000031
0120000042
0130000011
0130000022
0130000031
0130000044
0140000012
0140000021
0140000032
0140000043
0210000012
0210000022
0210000032
0210000044
0220000012
0220000021
0220000032
0220000043
0230000012
0230000023
0230000034
0230000041
0240000011
0240000024
0240000033
0240000042
0310000011
0310000024
0310000033
0310000044
0320000012
0320000023
0320000034
0320000043
0330000014
0330000023
0330000034
0330000043
0340000013
0340000023
0340000033
0340000043
0410000014
0410000023
0410000034
0410000043
0420000013
0420000024
0420000033
0420000044
0430000013
0430000024
0430000033
0430000042
0440000014
0440000024
0440000034
0440000042

Here is a p44 oscillator translated into this rule:

Code: Select all

x = 11, y = 1, rule = 1DD
AB5CA2CD!

Note that patterns in this 1D rule cannot in general be flipped left-right. The herring-bone scheme used to translate the pattern from the 2D CA to the 1D CA introduces a left-right asymmetry.

[ebcube]

p32 oscillator in 1DD (don't know how to translate it to Inverse Coagulations):

Code: Select all

x = 22, y = 1, rule = 1DD
2DBD2CBC5D2CA3CD2A!

[Paul Tooke]

ebcube wrote:

p32 oscillator in 1DD (don't know how to translate it to Inverse Coagulations

Ouch!! Three things occur to me;
Firstly: I obviously didn't name the table very well (I didn't mean the 1DD.table name to propogate publicly)
Secondly: Yes, this pattern is p32 in the rule table that I supplied. (i just hope that I didn't supply you with a wrong'un)
Thirdly, I do know how to do the translation. The comments in the rule table were supposed to explain how to do this, but they obviously weren't clear enough. My immediate manual attempts to translate this into B478/S234678 aren't working. But, it's late in my TZ and long after beer'o'clock with all which that may imply, so please bear with me until I take another look at this tomorrow. I really hope that I haven't posted a duff rules table.
Paul.

[Paul Tooke]

The good news is that ebcubes oscillator does translate into a p32 oscillator in B478/S234678 (shown here with the stator reduced a bit):

Code: Select all

x = 18, y = 18, rule = B478/S234678
3o$2obo$obo$bob3o$3b2obo$3bob3o$4b5o$5b5o$6b5o$7b5o$8b3obo$9bobo$10bob
obo$13bobo$12bobobo$13bobobo$14bob2o$15b3o!

The less welcome news is that I failed to heed my own admonition about the asymmetrical nature of the transformation to the 1D CA and as a result I managed to transpose the transitions that occur at the ends of the pattern. Thankfully, there were enough redundant stator cells at each end of this oscillator to prevent that from being a problem in this case.

Here is a corrected table file which now uses just 4 states and has a bit more explanation of how the transformation between the 2D and 1D CA works:

Code: Select all

n_states:4
neighborhood:Moore
symmetries:none

# 1-D CA emulated diagonally in B478/S23468
# 
# A pattern of the following form in B478/S234678:
#
# *............
# .*...........
# ..*AA..........
# ..A*BB.........
# ..AB*CC........
# ...BC*DD.......
# ....CD*EE......
# .....DE*FF.....
# ......EF*GG....
# .......FG*.....
# .......G..*...
#
# corresponds to the 1-D pattern:
#
# ..ABCDEFG..
#
# Where the 2D cell pattern to 1-D cell state is done according to the following scheme:
#
#  0 = #.. 1 = ##. 2 = #.# 3 = ###
#      .??     #??     .??     #??
#      .??     .??     #??     #??

0000000010
0000000020
0000000031
0100000001
0100000011
0100000021
0100000030
0200000000
0200000011
0200000023
0200000032
0300000003
0300000012
0300000022
0300000033
0010000000
0010000011
0010000021
0010000030
0110000001
0110000010
0110000022
0110000033
0210000003
0210000012
0210000022
0210000032
0310000002
0310000013
0310000023
0310000033
0020000000
0020000010
0020000020
0020000031
0120000001
0120000011
0120000023
0120000032
0220000002
0220000013
0220000023
0220000032
0320000003
0320000012
0320000022
0320000033
0030000000
0030000011
0030000023
0030000032
0130000003
0130000012
0130000020
0130000031
0230000003
0230000012
0230000022
0230000032
0330000002
0330000013
0330000021
0330000031

Here is ebcubes oscillator as it would be encoded for the new table:

Code: Select all

x = 17, y = 1, rule = 1DD
CB.C3BA3BCB.2BA!