1 transition away from Brian's Brain (ruletable, 3-state OT)

[unname4798]

Discuss any rules 1 transition away from Brian's Brain (ruletable, 3-state OT).

[Banananananan]

Here is one! In this rule, the diagonal ship in Brian’s Brain can be extended like this:

Code: Select all

x = 6, y = 7, rule = /2-e/3
3.B$3.A.A$4.2B$B.AB.A$A2.BA$.2B$2.A!

This is a heavyweight variant.
Here is a middleweight variant too:

Code: Select all

x = 202, y = 202, rule = /2-e/3
148$139.BA$140.AB$138.B2.2A$139.B.B$140.A!

[unname4798]

Here is one! In this rule, the diagonal ship in Brian’s Brain can be extended like this:

Code: Select all

x = 6, y = 7, rule = /2-e/3
3.B$3.A.A$4.2B$B.AB.A$A2.BA$.2B$2.A!

This is a heavyweight variant.
Here is a middleweight variant too:

Code: Select all

x = 202, y = 202, rule = /2-e/3
148$139.BA$140.AB$138.B2.2A$139.B.B$140.A!

I said, 3-state OT RuleLoader!

[confocaloid]

Discuss any rules 1 transition away from Brian's Brain (ruletable, 3-state OT).

[...]
I said, 3-state OT RuleLoader!

You didn't really say that before now.

Not counting suboptimal choices of wording (which can be discussed elsewhere), I think you need to provide some more information about the rulespace you suggest to explore, if you want it to be well-defined.

When you say "Brian's Brain" and "ruletable", do you mean a Golly ruletable supported by the RuleLoader algo? What is the specific ruletable for Brian's Brain you have? Are variables allowed? Which cellular automata belong to the rulespace and which do not belong? How many distinct cellular automata belong to the rulespace, and how this number is calculated?

[unname4798]

Discuss any rules 1 transition away from Brian's Brain (ruletable, 3-state OT).

[...]
I said, 3-state OT RuleLoader!

You didn't really say that before now.

Not counting suboptimal choices of wording (which can be discussed elsewhere), I think you need to provide some more information about the rulespace you suggest to explore, if you want it to be well-defined.

When you say "Brian's Brain" and "ruletable", do you mean a Golly ruletable supported by the RuleLoader algo? What is the specific ruletable for Brian's Brain you have? Are variables allowed? Which cellular automata belong to the rulespace and which do not belong? How many distinct cellular automata belong to the rulespace, and how this number is calculated?

Ruletable:

Code: Select all

@RULE BB-RuleLoader
@TABLE
n_states:3
neighborhood:Moore
symmetries:permute
var a={0,1,2}
var b=a
var c=a
var d=a
var e=a
var f=a
var g=a
var h=a
var i={0,2}
var j=i
var k=i
var l=i
var m=i
var n=i
0,1,1,i,j,k,l,m,n,1
1,a,b,c,d,e,f,g,h,2
2,a,b,c,d,e,f,g,h,0

There are 256^256^9 ruletables. 2-state is a subset of 3-state. 3-state is a subset of 4-state, and so on.
For 3 states, the number is 3^3^9.

[tommyaweosme]

if it has exactly 4 neighbors then the generations stays

Code: Select all

x=0,y=0,rule=bb-4rs
!
@RULE bb-4rs
@TABLE
n_states:3
neighborhood:Moore
symmetries:permute
var a={0,1,2}
var b=a
var c=a
var d=a
var e=a
var f=a
var g=a
var h=a
var i={0,2}
var j=i
var k=i
var l=i
var m=i
var n=i
0,1,1,i,j,k,l,m,n,1
1,a,b,c,d,e,f,g,h,2
2,1,1,1,1,i,j,k,l,2
2,a,b,c,d,e,f,g,h,0

theres quite a few spaceships and rakes

edit:

Code: Select all

x = 12, y = 9, rule = bb-4rs
2$4.B$3.2A$4.B.B$5.A!
@RULE bb-4rs
@TABLE
n_states:3
neighborhood:Moore
symmetries:permute
var a={0,1,2}
var b=a
var c=a
var d=a
var e=a
var f=a
var g=a
var h=a
var i={0,2}
var j=i
var k=i
var l=i
var m=i
var n=i
0,1,1,i,j,k,l,m,n,1
1,a,b,c,d,e,f,g,h,2
2,1,1,1,1,i,j,k,l,2
2,a,b,c,d,e,f,g,h,0

[confocaloid]

Discuss any rules 1 transition away from Brian's Brain (ruletable, 3-state OT).

[...]
I said, 3-state OT RuleLoader!

You didn't really say that before now.

Not counting suboptimal choices of wording (which can be discussed elsewhere), I think you need to provide some more information about the rulespace you suggest to explore, if you want it to be well-defined.

When you say "Brian's Brain" and "ruletable", do you mean a Golly ruletable supported by the RuleLoader algo? What is the specific ruletable for Brian's Brain you have? Are variables allowed? Which cellular automata belong to the rulespace and which do not belong? How many distinct cellular automata belong to the rulespace, and how this number is calculated?

Ruletable:

Code: Select all

@RULE BB-RuleLoader
@TABLE
n_states:3
neighborhood:Moore
symmetries:permute
var a={0,1,2}
var b=a
var c=a
var d=a
var e=a
var f=a
var g=a
var h=a
var i={0,2}
var j=i
var k=i
var l=i
var m=i
var n=i
0,1,1,i,j,k,l,m,n,1
1,a,b,c,d,e,f,g,h,2
2,a,b,c,d,e,f,g,h,0

There are 256^256^9 ruletables. 2-state is a subset of 3-state. 3-state is a subset of 4-state, and so on.
For 3 states, the number is 3^3^9.

How the number 3^3^9 was obtained?

There are 9 cells in the range-1 Moore neighbourhood, each of which can be in one of three states. That means there are 3^9 possibilities for the current states of cells in the 3x3 neighbourhood (the fully specified condition).
For every possible fully specified condition, there are three possible choices of the future state of the middle cell (three possible choices of the rule to be applied in that case). That would give 3^3^9 possible three-state cellular automata with range-1 Moore neighbourhood, without any required symmetries (i.e. "symmetries: none").

The number of possible ruletables (that are supported by the RuleLoader algo and work in Golly and LifeViewer) is higher than that, because any given cellular automaton can be defined by many different ruletables. If you omit the requirement "...and work in Golly and LifeViewer" then there are infinitely many distinct ruletables -- you can always do some trivial change (e.g. rename a variable) to make a different ruletable.

The above means that the claims
>> "There are 256^256^9 ruletables. [...] For 3 states, the number is 3^3^9."
are incorrect.
However, even if you correct that to count cellular automata instead of ruletables, there are still some unresolved issues:

• Your ruletable "BB-RuleLoader" uses "symmetries: permute". That means permutations of current states of neighbours are considered equivalent. With three cellstates, the condition can be fully specified by writing down the current state of the middle cell, the number of state-1 neighbours, and the number of state-2 neighbours.
  However, you posted the numbers 256^256^9 and 3^3^9, i.e. you are apparently trying to count CA that could be implemented via ruletables with "symmetries: none" instead.
  Where is an error? Is it in the ruletable, or in the numbers you posted, or both?
• Asking again: are variables allowed?
  For example, I can start from your ruletable for Brian's Brain, prepend the line

  Code: Select all

  0,  a, a, a, a, b, b, b, b, 2

  which defines the transition rule "a state-0 cell becomes a state-2 cell if there are four state-a neighbours and four state-b neighbours for some (not necessarily distinct) choices of a and b", and claim that that is on-topic here. Would the resulting cellular automaton be on-topic here? Again, what is the exact rulespace to be explored in this thread?

[unname4798]

You didn't really say that before now.

Not counting suboptimal choices of wording (which can be discussed elsewhere), I think you need to provide some more information about the rulespace you suggest to explore, if you want it to be well-defined.

When you say "Brian's Brain" and "ruletable", do you mean a Golly ruletable supported by the RuleLoader algo? What is the specific ruletable for Brian's Brain you have? Are variables allowed? Which cellular automata belong to the rulespace and which do not belong? How many distinct cellular automata belong to the rulespace, and how this number is calculated?

Ruletable:

Code: Select all

@RULE BB-RuleLoader
@TABLE
n_states:3
neighborhood:Moore
symmetries:permute
var a={0,1,2}
var b=a
var c=a
var d=a
var e=a
var f=a
var g=a
var h=a
var i={0,2}
var j=i
var k=i
var l=i
var m=i
var n=i
0,1,1,i,j,k,l,m,n,1
1,a,b,c,d,e,f,g,h,2
2,a,b,c,d,e,f,g,h,0

There are 256^256^9 ruletables. 2-state is a subset of 3-state. 3-state is a subset of 4-state, and so on.
For 3 states, the number is 3^3^9.

How the number 3^3^9 was obtained?

There are 9 cells in the range-1 Moore neighbourhood, each of which can be in one of three states. That means there are 3^9 possibilities for the current states of cells in the 3x3 neighbourhood (the fully specified condition).
For every possible fully specified condition, there are three possible choices of the future state of the middle cell (three possible choices of the rule to be applied in that case). That would give 3^3^9 possible three-state cellular automata with range-1 Moore neighbourhood, without any required symmetries (i.e. "symmetries: none").

The number of possible ruletables (that are supported by the RuleLoader algo and work in Golly and LifeViewer) is higher than that, because any given cellular automaton can be defined by many different ruletables. If you omit the requirement "...and work in Golly and LifeViewer" then there are infinitely many distinct ruletables -- you can always do some trivial change (e.g. rename a variable) to make a different ruletable.

The above means that the claims
>> "There are 256^256^9 ruletables. [...] For 3 states, the number is 3^3^9."
are incorrect.
However, even if you correct that to count cellular automata instead of ruletables, there are still some unresolved issues:

• Your ruletable "BB-RuleLoader" uses "symmetries: permute". That means permutations of current states of neighbours are considered equivalent. With three cellstates, the condition can be fully specified by writing down the current state of the middle cell, the number of state-1 neighbours, and the number of state-2 neighbours.
  However, you posted the numbers 256^256^9 and 3^3^9, i.e. you are apparently trying to count CA that could be implemented via ruletables with "symmetries: none" instead.
  Where is an error? Is it in the ruletable, or in the numbers you posted, or both?
• Asking again: are variables allowed?
  For example, I can start from your ruletable for Brian's Brain, prepend the line

  Code: Select all

  0,  a, a, a, a, b, b, b, b, 2

  which defines the transition rule "a state-0 cell becomes a state-2 cell if there are four state-a neighbours and four state-b neighbours for some (not necessarily distinct) choices of a and b", and claim that that is on-topic here. Would the resulting cellular automaton be on-topic here? Again, what is the exact rulespace to be explored in this thread?

Sorry, I miscalculated.

[olivia enessemir]

Within the following rule:

Code: Select all

@RULE BB-2B1_2
@TABLE
n_states:3
neighborhood:Moore
symmetries:permute
var a={0,1,2}
var b=a
var c=a
var d=a
var e=a
var f=a
var g=a
var h=a
var i={0,2}
var j=i
var k=i
var l=i
var m=i
var n=i
0,1,1,i,j,k,l,m,n,1
0,0,0,0,0,0,1,2,2,2
1,a,b,c,d,e,f,g,h,2
2,a,b,c,d,e,f,g,h,0

there are some mildly interesting patterns

Code: Select all

x = 8, y = 11, rule = BB-2B1_2
.B2ABA$2.B.B.B$B.B.ABA$AB2A.A$.A.AB$2.B.A$2.AB$3.AB$4.A2.B$5.2BA$5.2A
!

(it is of note that the c/4d does not evolve the same way it does in Brian's Brain and in particular lacks glide symmetry.)