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PlusSumA

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PlusSumA

Posted: December 4th, 2012, 6:51 pm
by Extrementhusiast
I have just found a member of a family of rules. What's special about this member is that it falls into Class IV (by my judgment). Here is the table for the whole family, with the relevant rule selected:

Code: Select all

n_states:4
neighborhood:vonNeumann
symmetries:permute

var a={0,1,2,3}
var b={a}
var c={a}
var d={a}

# B12
# 0,3,3,3,3,1
# 1,3,3,3,3,2
# 2,3,3,3,3,3

# B11
# 0,2,3,3,3,1
# 1,2,3,3,3,2
# 2,2,3,3,3,3

# B10
# 0,1,3,3,3,1
# 0,2,2,3,3,1
# 1,1,3,3,3,2
# 1,2,2,3,3,2
# 2,1,3,3,3,3
# 2,2,2,3,3,3

# B9
# 0,0,3,3,3,1
# 0,1,2,3,3,1
# 0,2,2,2,3,1
# 1,0,3,3,3,2
# 1,1,2,3,3,2
# 1,2,2,2,3,2
# 2,0,3,3,3,3
# 2,1,2,3,3,3
# 2,2,2,2,3,3

# B8
# 0,0,2,3,3,1
# 0,1,1,3,3,1
# 0,1,2,2,3,1
# 0,2,2,2,2,1
# 1,0,2,3,3,2
# 1,1,1,3,3,2
# 1,1,2,2,3,2
# 1,2,2,2,2,2
# 2,0,2,3,3,3
# 2,1,1,3,3,3
# 2,1,2,2,3,3
# 2,2,2,2,2,3

# B7
0,0,1,3,3,1
0,0,2,2,3,1
0,1,1,2,3,1
0,1,2,2,2,1
1,0,1,3,3,2
1,0,2,2,3,2
1,1,1,2,3,2
1,1,2,2,2,2
2,0,1,3,3,3
2,0,2,2,3,3
2,1,1,2,3,3
2,1,2,2,2,3

# B6
# 0,0,0,3,3,1
# 0,0,1,2,3,1
# 0,0,2,2,2,1
# 0,1,1,1,3,1
# 0,1,1,2,2,1
# 1,0,0,3,3,2
# 1,0,1,2,3,2
# 1,0,2,2,2,2
# 1,1,1,1,3,2
# 1,1,1,2,2,2
# 2,0,0,3,3,3
# 2,0,1,2,3,3
# 2,0,2,2,2,3
# 2,1,1,1,3,3
# 2,1,1,2,2,3

# B5
# 0,0,0,2,3,1
# 0,0,1,1,3,1
# 0,0,1,2,2,1
# 0,1,1,1,2,1
# 1,0,0,2,3,2
# 1,0,1,1,3,2
# 1,0,1,2,2,2
# 1,1,1,1,2,2
# 2,0,0,2,3,3
# 2,0,1,1,3,3
# 2,0,1,2,2,3
# 2,1,1,1,2,3

# B4
# 0,0,0,1,3,1
# 0,0,0,2,2,1
# 0,0,1,1,2,1
# 0,1,1,1,1,1
# 1,0,0,1,3,2
# 1,0,0,2,2,2
# 1,0,1,1,2,2
# 1,1,1,1,1,2
# 2,0,0,1,3,3
# 2,0,0,2,2,3
# 2,0,1,1,2,3
# 2,1,1,1,1,3

# B3
# 0,0,0,0,3,1
# 0,0,0,1,2,1
# 0,0,1,1,1,1
# 1,0,0,0,3,2
# 1,0,0,1,2,2
# 1,0,1,1,1,2
# 2,0,0,0,3,3
# 2,0,0,1,2,3
# 2,0,1,1,1,3

# B2
0,0,0,0,2,1
0,0,0,1,1,1
1,0,0,0,2,2
1,0,0,1,1,2
2,0,0,0,2,3
2,0,0,1,1,3

# B1
# 0,0,0,0,1,1
# 1,0,0,0,1,2
# 2,0,0,0,1,3

# S12
# 1,3,3,3,3,1
# 2,3,3,3,3,2
# 3,3,3,3,3,3

# S11
# 1,2,3,3,3,1
# 2,2,3,3,3,2
# 3,2,3,3,3,3

# S10
# 1,1,3,3,3,1
# 1,2,2,3,3,1
# 2,1,3,3,3,2
# 2,2,2,3,3,2
# 3,1,3,3,3,3
# 3,2,2,3,3,3

# S9
# 1,0,3,3,3,1
# 1,1,2,3,3,1
# 1,2,2,2,3,1
# 2,0,3,3,3,2
# 2,1,2,3,3,2
# 2,2,2,2,3,2
# 3,0,3,3,3,3
# 3,1,2,3,3,3
# 3,2,2,2,3,3

# S8
1,0,2,3,3,1
1,1,1,3,3,1
1,1,2,2,3,1
1,2,2,2,2,1
2,0,2,3,3,2
2,1,1,3,3,2
2,1,2,2,3,2
2,2,2,2,2,2
3,0,2,3,3,3
3,1,1,3,3,3
3,1,2,2,3,3
3,2,2,2,2,3

# S7
# 1,0,1,3,3,1
# 1,0,2,2,3,1
# 1,1,1,2,3,1
# 1,1,2,2,2,1
# 2,0,1,3,3,2
# 2,0,2,2,3,2
# 2,1,1,2,3,2
# 2,1,2,2,2,2
# 3,0,1,3,3,3
# 3,0,2,2,3,3
# 3,1,1,2,3,3
# 3,1,2,2,2,3

# S6
1,0,0,3,3,1
1,0,1,2,3,1
1,0,2,2,2,1
1,1,1,1,3,1
1,1,1,2,2,1
2,0,0,3,3,2
2,0,1,2,3,2
2,0,2,2,2,2
2,1,1,1,3,2
2,1,1,2,2,2
3,0,0,3,3,3
3,0,1,2,3,3
3,0,2,2,2,3
3,1,1,1,3,3
3,1,1,2,2,3

# S5
# 1,0,0,2,3,1
# 1,0,1,1,3,1
# 1,0,1,2,2,1
# 1,1,1,1,2,1
# 2,0,0,2,3,2
# 2,0,1,1,3,2
# 2,0,1,2,2,2
# 2,1,1,1,2,2
# 3,0,0,2,3,3
# 3,0,1,1,3,3
# 3,0,1,2,2,3
# 3,1,1,1,2,3

# S4
1,0,0,1,3,1
1,0,0,2,2,1
1,0,1,1,2,1
1,1,1,1,1,1
2,0,0,1,3,2
2,0,0,2,2,2
2,0,1,1,2,2
2,1,1,1,1,2
3,0,0,1,3,3
3,0,0,2,2,3
3,0,1,1,2,3
3,1,1,1,1,3

# S3
# 1,0,0,0,3,1
# 1,0,0,1,2,1
# 1,0,1,1,1,1
# 2,0,0,0,3,2
# 2,0,0,1,2,2
# 2,0,1,1,1,2
# 3,0,0,0,3,3
# 3,0,0,1,2,3
# 3,0,1,1,1,3

# S2
# 1,0,0,0,2,1
# 1,0,0,1,1,1
# 2,0,0,0,2,2
# 2,0,0,1,1,2
# 3,0,0,0,2,3
# 3,0,0,1,1,3

# S1
# 1,0,0,0,1,1
# 2,0,0,0,1,2
# 3,0,0,0,1,3

# S0
# 1,0,0,0,0,1
# 2,0,0,0,0,2
# 3,0,0,0,0,3

# Else
1,a,b,c,d,0
2,a,b,c,d,1
3,a,b,c,d,2
A cleaned-up version will follow. Save this or the cleaned-up version as "plussuma.table".

Re: PlusSumA

Posted: December 4th, 2012, 6:53 pm
by Extrementhusiast
Cleaned-up version:

Code: Select all

n_states:4
neighborhood:vonNeumann
symmetries:permute

var a={0,1,2,3}
var b={a}
var c={a}
var d={a}

0,0,1,3,3,1
0,0,2,2,3,1
0,1,1,2,3,1
0,1,2,2,2,1
1,0,1,3,3,2
1,0,2,2,3,2
1,1,1,2,3,2
1,1,2,2,2,2
2,0,1,3,3,3
2,0,2,2,3,3
2,1,1,2,3,3
2,1,2,2,2,3
0,0,0,0,2,1
0,0,0,1,1,1
1,0,0,0,2,2
1,0,0,1,1,2
2,0,0,0,2,3
2,0,0,1,1,3
1,0,2,3,3,1
1,1,1,3,3,1
1,1,2,2,3,1
1,2,2,2,2,1
2,0,2,3,3,2
2,1,1,3,3,2
2,1,2,2,3,2
2,2,2,2,2,2
3,0,2,3,3,3
3,1,1,3,3,3
3,1,2,2,3,3
3,2,2,2,2,3
1,0,0,3,3,1
1,0,1,2,3,1
1,0,2,2,2,1
1,1,1,1,3,1
1,1,1,2,2,1
2,0,0,3,3,2
2,0,1,2,3,2
2,0,2,2,2,2
2,1,1,1,3,2
2,1,1,2,2,2
3,0,0,3,3,3
3,0,1,2,3,3
3,0,2,2,2,3
3,1,1,1,3,3
3,1,1,2,2,3
1,0,0,1,3,1
1,0,0,2,2,1
1,0,1,1,2,1
1,1,1,1,1,1
2,0,0,1,3,2
2,0,0,2,2,2
2,0,1,1,2,2
2,1,1,1,1,2
3,0,0,1,3,3
3,0,0,2,2,3
3,0,1,1,2,3
3,1,1,1,1,3
1,a,b,c,d,0
2,a,b,c,d,1
3,a,b,c,d,2

Re: PlusSumA

Posted: December 5th, 2012, 5:31 am
by Kasuha
Interesting rule, but is there a reason to stop at state 3?
With B...7/S...8, highest theoretically reachable state is about 15 (cell state can continue to grow as long as neighbors are held at favorable sum, but as soon as its state exceeds maximum S value they start dying out; they can still support the cell's growth until they fall below lowest B rule).
Or if we cap it at 3, why don't birth rules make the state 3 stay?

Re: PlusSumA

Posted: December 6th, 2012, 3:56 pm
by Extrementhusiast
Essentially, birth increments the state, survival keeps the state, while death decrements the state. It's the same with the original GoL, except with more states.

Re: PlusSumA

Posted: December 6th, 2012, 4:15 pm
by Kasuha
Extrementhusiast wrote:Essentially, birth increments the state, survival keeps the state, while death decrements the state. It's the same with the original GoL, except with more states.
Yes I got it... my concern was that your table uses fewer states than what the rule supports and that the birth rule does not apply to highest state which gets a death instead. It sounds illogical to me so I wondered if it was intent, e.g. to make the resulting CA better in some way.

Re: PlusSumA

Posted: December 7th, 2012, 5:33 pm
by Extrementhusiast
Nope. The four states are numbered 0,1,2,3.

Re: PlusSumA

Posted: December 7th, 2012, 7:13 pm
by Kasuha
Extrementhusiast wrote:Nope. The four states are numbered 0,1,2,3.
You're welcome.

Re: PlusSumA

Posted: December 31st, 2012, 5:00 pm
by Extrementhusiast
Found a sparky (and messy) puffer engine:

Code: Select all

x = 13, y = 13, rule = plussuma
8.A$6.A.2A$3.A2.A2.A$2.BA.B2.4A$2.A.BAB.2A.2A2$2.A3.B.B.2A$4.AB2.AB$
2.B.2A2.B$3AC5.2A$2.BAB.A.AB$BA.A$AB.A!
Not sure what could be done with this.

(Diagonally symmetric patterns seem to explode more often than non-diagonally symmetric ones.)
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