Thread for advanced questions

[Vort]

How to make hash for pattern on torus, which is not only orientation-independent, but also position-independent?

[wirehead]

How to make hash for pattern on torus, which is not only orientation-independent, but also position-independent?

Probably the best way to do it would be to just enumerate all of the unique shifts of the repeating unit and then find the canonical apgcode of each and then choose the one with the shortest or dictionary-first apgcode. apgcodes already canonicalize the orientation of a pattern (see Apgcode#Canonical_form)

[Vort]

Thanks for the answer.
I thought about similar approach:
Just hash all N x M x 8 variations and XOR hashes together.
It is, however, too slow for the thing I was trying to do (random soup searches) and becomes totally impractical really quick. For example, hashing 1000x1000 pattern will take seconds of computing time.
I ended up just using simple hashes for all variations and linking them all to a single object, which represents orientation and position independent pattern.
But if someone finds practical method for hash calculation, it may be useful nevertheless, for future projects.

[B468S02357]

Of the of the with and the is golly and the is rules and so how the do so and is the with and but so yet with the and the Repsplosion the into golly i cant?
Edit: I tried to do it with figuring the out the out the out the out the out the out and with of the golly and it says but the .rule and i am not knowing how to the .rule???

[NNlk05]

Of the of the with and the is golly and the is rules and so how the do so and is the with and but so yet with the and the Repsplosion the into golly i cant?

???

[hotdogPi]

I know it's difficult to parse the question above, but they're asking how to put an alternating rule into Golly. I believe it requires a ruletable, which I'm not familiar with myself.

[MDA]

To make an alternating ruletable, you build separate ruletables for each rule you want to alternate (using state 1 for the first and state 2 for the second) and combine them so that all birth/survival conditions in rule 1 generate state-2 cells, and all birth/survival conditions in rule 2 generate state-1 cells. You should make state 1 and state 2 cells the same color.

An example, built from one of B468S02357’s alternating rules:

Code: Select all

@RULE Alt


@COLORS
0 000 000 000
1 255 255 255
2 255 255 255

@TABLE
neighborhood: Moore
symmetries: rotate4reflect
n_states: 3

var a={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={0,1,2}
var j=i
var k=i
var l=i
var m=i
var n=i
var o=i
var p=i
var q=i

# B2a/S05

0,1,1,0,0,0,0,0,0,2

1,0,0,0,0,0,0,0,0,2

1,1,1,1,0,1,0,1,0,2
1,0,1,1,1,0,1,0,1,2
1,0,1,1,0,1,1,0,1,2
1,0,1,1,1,1,1,0,0,2
1,1,1,1,1,1,0,0,0,2
1,1,0,1,1,1,1,0,0,2
1,0,1,1,0,1,0,1,1,2
1,1,1,1,0,1,1,0,0,2
1,1,1,1,1,0,1,0,0,2
1,1,1,0,1,1,1,0,0,2

1,i,j,k,l,m,n,o,p,0

# B2-a3/S2456

0,0,2,0,2,0,0,0,0,1
0,2,0,2,0,0,0,0,0,1
0,2,0,0,2,0,0,0,0,1
0,2,0,0,0,2,0,0,0,1
0,0,2,0,0,0,2,0,0,1

0,0,2,0,2,0,2,0,0,1
0,2,0,2,0,2,0,0,0,1
0,2,0,2,0,0,2,0,0,1
0,2,2,2,0,0,0,0,0,1
0,2,2,0,0,0,0,0,2,1
0,2,2,0,2,0,0,0,0,1
0,2,0,0,2,0,2,0,0,1
0,2,2,0,0,0,2,0,0,1
0,2,2,0,0,0,0,2,0,1
0,2,2,0,0,2,0,0,0,1

2,0,2,0,2,0,0,0,0,1
2,2,0,2,0,0,0,0,0,1
2,2,0,0,2,0,0,0,0,1
2,2,2,0,0,0,0,0,0,1
2,2,0,0,0,2,0,0,0,1
2,0,2,0,0,0,2,0,0,1

2,0,2,0,2,0,2,0,2,1
2,2,0,2,0,2,0,2,0,1
2,2,0,2,2,0,2,0,0,1
2,2,2,2,2,0,0,0,0,1
2,2,2,0,2,2,0,0,0,1
2,0,2,2,2,0,2,0,0,1
2,2,2,0,2,0,2,0,0,1
2,2,2,2,0,0,2,0,0,1
2,2,0,2,0,2,2,0,0,1
2,2,2,2,0,2,0,0,0,1
2,2,0,0,2,2,2,0,0,1
2,0,2,2,0,2,2,0,0,1
2,0,2,2,0,0,2,2,0,1

2,2,2,2,0,2,0,2,0,1
2,0,2,2,2,0,2,0,2,1
2,0,2,2,0,2,2,0,2,1
2,0,2,2,2,2,2,0,0,1
2,2,2,2,2,2,0,0,0,1
2,2,0,2,2,2,2,0,0,1
2,0,2,2,0,2,0,2,2,1
2,2,2,2,0,2,2,0,0,1
2,2,2,2,2,0,2,0,0,1
2,2,2,0,2,2,2,0,0,1

2,2,2,2,2,2,0,2,0,1
2,0,2,2,2,2,2,0,2,1
2,0,2,2,2,2,0,2,2,1
2,2,2,2,2,2,2,0,0,1
2,0,2,2,2,0,2,2,2,1
2,2,2,2,0,2,2,2,0,1

2,i,j,k,l,m,n,o,p,0

[synperiplanar]

apparently i was using the spanish keyboard here and didn't notice so here's the actual question i was asking

i'm pretty sure it can be proven pretty easily that the maximum amount of cells from one generation to the next in B3/S23 is 3p, where p is the population at the before-generation.
here are some agars that showcase this maximum:

Code: Select all

x = 7, y = 9, rule = B3/S23:T9,9
o2bo2bo$o2bo2bo$o2bo2bo$o2bo2bo$o2bo2bo$o2bo2bo$o2bo2bo$o2bo2bo$o2bo2b
o!
[[ SHOWGENSTATS ]]

Code: Select all

x = 9, y = 9, rule = B3/S23:T9,9
bo2bo2bo$2bo2bo2bo$o2bo2bo$bo2bo2bo$2bo2bo2bo$o2bo2bo$bo2bo2bo$2bo2bo
2bo$o2bo2bo!
[[ SHOWGENSTATS ]]

Code: Select all

x = 9, y = 9, rule = B3/S23:T9,9
bo2bo2bo$o2bo2bo$o2bo2bo$2bo2bo2bo$2bo2bo2bo$bo2bo2bo$bo2bo2bo$o2bo2b
o$o2bo2bo!
[[ SHOWGENSTATS ]]

now, what about extending this question to ask what the maximum amount of cells from one generation to two generations after is in B3/S23? what about three generations, four generation, and so on?

[MDA]

Are there any known "American Dream"-like still-lives which are finite yet have only themselves and infinitely large patterns as predecessors?

[otismo]

Somehow I do not have Phil Bookman's Still-Life Pattern Collection -

can anyone help me out - PHPBB12345 . . .

Maximum density of 21x21 still lifes (symmetric variant):

Code: Select all

x = 21, y = 21, rule = B3/S23
2ob2obob2ob2obob2ob2o$2obob3obobob3obob2o$3bo5bobo5bo$3ob5obob5ob3o$o
2bo4bobobo4bo2bo$bobob2obobobob2obobo$2obob2obobobob2obob2o$bobo4bobob
o4bobo$o2b6obob6o2bo$3o7bo7b3o$3b7ob7o$3o7bo7b3o$o2b6obob6o2bo$bobo4bo
bobo4bobo$2obob2obobobob2obob2o$bobob2obobobob2obobo$o2bo4bobobo4bo2bo
$3ob5obob5ob3o$3bo5bobo5bo$2obob3obobob3obob2o$2ob2obob2ob2obob2ob2o!

EDIT: 13x13

Code: Select all

x = 13, y = 13, rule = B3/S23
2ob2obob2ob2o$2obob3obob2o$3bo5bo$3ob5ob3o$o2bo5bo2bo$bobo2b2obobo$2ob
obobobob2o$bobob2o2bobo$o2bo5bo2bo$3ob5ob3o$3bo5bo$2obob3obob2o$2ob2ob
ob2ob2o!

15x15:

Code: Select all

x = 15, y = 15, rule = B3/S23
ob2ob2obob2ob2o$2obobob3obobo$3bobo5bobo$2obob7ob2o$bobo9bo$o2b9o2bo$
3o9b3o$3b9o$3o9b3o$o2b9o2bo$bo9bobo$2ob7obob2o$bobo5bobo$bobob3obobob
2o$2ob2obob2ob2obo!

14x14:

Code: Select all

x = 14, y = 14, rule = B3/S23
2ob2ob2ob2ob2o$2ob2ob2ob2ob2o2$2ob8ob2o$2obo6bob2o$3bob4obo$2obobo2bob
ob2o$2obobo2bobob2o$3bob4obo$2obo6bob2o$2ob8ob2o2$2ob2ob2ob2ob2o$2ob2o
b2ob2ob2o!