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.