Endemic periodic patterns and still lifes

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
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Freywa
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Endemic periodic patterns and still lifes

Post by Freywa » June 23rd, 2019, 6:30 am

Some months ago I asked this question:
What is the smallest periodic pattern by number of cells that is endemic (exact evolutionary sequence is unique) to B3/S23? The pattern does not have to be indecomposable into smaller periodic patterns (i.e. it can be pseudo).
I noted that the 2-engine Cordership is endemic, so the answer was at most 100 cells, but then I found that 60P312 + Gabriel's p138 achieves 96 cells, and this is the smallest endemic pattern I know of:

Code: Select all

x = 95, y = 42, rule = B3/S23
20b2o$20b2o5$18b2o$19bo$6bo12bo15bo$5bobo10bo15bobo$5bobo26bobo$6bo28b
o46b3o$81bo2bo$81bo2bo$81b2o4$6bo2bo81b3o$6b3o82bo2bo$2o38b2o52bo$2o
38b2o32b3o15b3o$33b3o38bo$32bo2bo38bo2bo$75b3o4$86b2o$84bo2bo$6bo28bo
48bo2bo$5bobo26bobo47b3o$5bobo15bo10bobo$6bo15bo12bo$22bo$22b2o5$20b2o
$20b2o!
After asking that question I asked a (hopefully) simpler one:
What is the smallest still life by number of cells whose cells exercise all S2 and S3 transitions, thus having a minrule containing S23 per se? Strict and pseudo should be considered separately.
It is trivial to derive a lower bound of 19 cells – there are 16 S2 and S3 transitions, but the S3a transition can only happen in a block.
Princess of Science, Parcly Taxel

Code: Select all

x = 31, y = 5, rule = B2-a/S12
3bo23bo$2obo4bo13bo4bob2o$3bo4bo13bo4bo$2bo4bobo11bobo4bo$2bo25bo!

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Saka
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Re: Endemic periodic patterns and still lifes

Post by Saka » June 23rd, 2019, 9:04 am

29 cell still life by gmc_nxtman on discord that contains all S23 transitions.

Code: Select all

29:
x = 11, y = 8, rule = B3/S23
2b2o$3bo$2bo5b2o$bo3bo2b2o$ob4o$bo4b4o$2b3o2bo2bo$4b2o3b2o!
EDIT:
If the still life doesnt have to be strict, then 24 bits is enough, 3 exmaples, by gmc_nxtman too

Code: Select all

x = 40, y = 11, rule = B3/S23
2b2o13b2o15b2o$2b2o13b2o15b2o2$2b2o13b2o15b2o$3bo14bo13bo2b3o$2bo13bo
2b2o11b2o4bo$bo3bo10b2obo14b4obo$ob4o11bobo2b2o10bo3bo$bo4b2o9bobobobo
13bo$2b3o2bo10bobo15bo$4b2o13bo16b2o!

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Re: Endemic periodic patterns and still lifes

Post by GUYTU6J » February 2nd, 2020, 11:48 am

(Found the thread by dvgrn's direction; see basic questions thread)
The China Labyrinth problem asks for a pattern consisting of 64 hexagons, any one of which has a unique neighbourhood configuration. One of the suggested solutions is:

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x = 14, y = 15, rule = B/S0123456H
4bo$4b4o$3b5o$4b2ob2o$5bob4o$5bo5bo$o2b3o5bo$b3o$b2obo4b2o2bo$bob3o3b
5o$2b2obo4b2obo$3b4o3bo$5bobob3obo$6bo$7b2o!
#C [[ VIEWONLY GRID THUMBNAIL THUMBSIZE 3 ]]
In other words, the pattern is able to identify the survival conditions of a 2-state range-1 cellular automaton on a hexagonal grid. Neglecting births, run it by one generation and we can check whether the rule is totalistic, isotropic or not.
The article considers two kinds of solutions to the original problem, "transcendental solutions" and "compact solutions". For our purpose we're interested in the transcendental ones, because in compact solutions the assigned neighbourhood may not coincide with the actual neighbourhood.
So naturally we consider analogies for other grids, other neighbourhoods and other ranges...(Yes we are somewhat far from CGoL)
For range-1 Von Neumann neighbourhood on a square grid, a solution is also given:

Code: Select all

x = 5, y = 5, rule = B/S01234V
o2b2o$5o$ob2o$3bo$ob3o!
#C [[ VIEWONLY GRID THUMBNAIL THUMBSIZE 3 ]]
However, when it comes to Moore neighbourhood, known as The Octopuszle on that website, no solution is provided for our purpose. There's a statement saying
Transcendental solutions proved not too difficult, but then, not too interesting either for lack of applications.
Let's start finding minimal still lives with isorulemin S012345678. Can we do it with S2i/2n/6i/6n used only twice each?

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Re: Endemic periodic patterns and still lifes

Post by Hdjensofjfnen » February 3rd, 2020, 1:06 pm

GUYTU6J wrote:
February 2nd, 2020, 11:48 am
Let's start finding minimal still lives with isorulemin S012345678. Can we do it with S2i/2n/6i/6n used only twice each?
That's not exactly the same problem: the China labyrinth problem was considering S2pH in one direction to be different than S2pH in another. S2pH showed up a total of 3 times.

Code: Select all

x = 5, y = 9, rule = B3-jqr/S01c2-in3
3bo$4bo$o2bo$2o2$2o$o2bo$4bo$3bo!

Code: Select all

x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!

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Re: Endemic periodic patterns and still lifes

Post by Moosey » February 3rd, 2020, 9:04 pm

Hdjensofjfnen wrote:
February 3rd, 2020, 1:06 pm
GUYTU6J wrote:
February 2nd, 2020, 11:48 am
Let's start finding minimal still lives with isorulemin S012345678. Can we do it with S2i/2n/6i/6n used only twice each?
That's not exactly the same problem: the China labyrinth problem was considering S2pH in one direction to be different than S2pH in another. S2pH showed up a total of 3 times.
Perhaps it would then be "nonisorulemin" S012345678
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Re: Endemic periodic patterns and still lifes

Post by GUYTU6J » May 18th, 2020, 10:48 pm

Freywa wrote:
June 23rd, 2019, 6:30 am
Some months ago I asked this question:
What is the smallest periodic pattern by number of cells that is endemic (exact evolutionary sequence is unique) to B3/S23? The pattern does not have to be indecomposable into smaller periodic patterns (i.e. it can be pseudo).
I noted that the 2-engine Cordership is endemic, so the answer was at most 100 cells, but then I found that 60P312 + Gabriel's p138 achieves 96 cells, and this is the smallest endemic pattern I know of:

Code: Select all

x = 95, y = 42, rule = B3/S23
20b2o$20b2o5$18b2o$19bo$6bo12bo15bo$5bobo10bo15bobo$5bobo26bobo$6bo28b
o46b3o$81bo2bo$81bo2bo$81b2o4$6bo2bo81b3o$6b3o82bo2bo$2o38b2o52bo$2o
38b2o32b3o15b3o$33b3o38bo$32bo2bo38bo2bo$75b3o4$86b2o$84bo2bo$6bo28bo
48bo2bo$5bobo26bobo47b3o$5bobo15bo10bobo$6bo15bo12bo$22bo$22b2o5$20b2o
$20b2o!
Improved to 86 cells with a stabilized period-184 glider gun:

Code: Select all

x = 81, y = 35, rule = B3/S23
26bo$24b3o$23bo$23b2o2$28bo$28bobo$27bobo$29bo2$70b3o$70bo2bo$70bo2bo$
72b2o2$33b2o$33bo$31bobo27b3o$12b2o17b2o27bo2bo$12bob2o44bo$15bo44b3o
15b3o$13bobo64bo$13b2o62bo2bo$2b2o73b3o$bobo$bo$2o$7bo59b2o$5b2o60bo2b
o$7b2o58bo2bo$6bo61b3o$17b2o$18bo$15b3o$15bo!
(EDIT on June 6: 84 cells with boat-bits

Code: Select all

x = 85, y = 39, rule = B3/S23
21b2o$22bo$21bo$21b2o6$32bo$32bobo$31bobo$33bo2$74b3o$74bo2bo$74bo2bo$
76b2o2$37b2o$37bo$ob2o31bobo27b3o$2obo12b2o17b2o27bo2bo$16bob2o44bo$
19bo44b3o15b3o$17bobo64bo$17b2o62bo2bo$81b3o4$11bo59b2o$9b2o60bo2bo$
11b2o58bo2bo$10bo61b3o$21b2o$22bo$19b3o$19bo!
)
Coupled with an oscillator that disallows B8 and S6e and is under 18 cells, this can make a new record.

Code: Select all

x = 42, y = 39, rule = B3/S23
14bo$14b3o$17bo19b4o$16b2o18bo4bo$35bobo3bo$34bobo3bo$34bo$34bo$34bo2b
o$35b2o10$18bo$16bo2bo$16bo3bo9bo$15bo4bo8bobo$15bo4bo8bobo$19bo$16b3o
4$5b2o$5b2o3$5b3o$2o2bob2o$2o2b2o18b2o$4b2o18bo$25b3o$27bo!
Last edited by GUYTU6J on June 6th, 2020, 1:04 am, edited 1 time in total.

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Re: Endemic periodic patterns and still lifes

Post by toroidalet » May 20th, 2020, 7:52 pm

If you can find a variation of this pattern where the spark-glider collision prevents S4c, that would improve the bound to 72 or 74 (minimum population in the odd phase)

Code: Select all

x = 49, y = 51, rule = B3/S23
17b2o$2o15bobo7b2o$2o17bo7b2o$17b3o4$17b3o$2o17bo$2o15bobo$17b2o10$43b
2o$43bo$41bobo$41b2o8$47b2o$47bo$45bobo$26b2o17b2o$26bob2o$29bo$27bobo
$27b2o$16b2o$15bobo$15bo$14b2o$21bo$19b2o$21b2o$20bo$31b2o$32bo$29b3o$
29bo!
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Re: Endemic periodic patterns and still lifes

Post by GUYTU6J » July 26th, 2021, 11:21 pm

Bump! The recent 66-cell p196 pi-heptomino hassler works only in Life and Pedestrian Life, so a pentadecathlon can be added to prevent B8, yielding a 78-cell solution:

Code: Select all

x = 34, y = 34, rule = B3/S23
bo27bo$bo26bobo$obo16b2o7bobo$bo17b2o6b2ob3o$bo31bo$bo25b2ob3o$bo25b2o
bo$obo$bo$bo4$25bo4b2o$24b3o3b2o$24bobo3$7bobo$2b2o3b3o$2b2o4bo7$3bob
2o$b3ob2o$o$b3ob2o6b2o$3bobo7b2o$3bobo$4bo!
Results from the ongoing SKOP project will be helpful for this topic.

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Patterns that only work in 1 rule

Post by squareroot12621 » April 17th, 2022, 11:36 am

I've had a thought lately: Are there any patterns* that only work in one rule? I can't stop thinking about it.
There are 3 difficulties:
  1. Outer-totalistic rules,
  2. isotropic non-totalistic rules, and
  3. non-isotropic rules.
For outer-totalistic rules, I found the oscillator p32 blinker hassler, which, apparently, only works in CGoL.
The rule does not have to be CGoL.
*Patterns are subdivided into these five groups: still lifes, oscillators, spaceships, puffers/rakes/guns, and anything else.

Quick edit: I am not sure if this should go in Patterns or OCA. :|

Code: Select all

4b8o$4b8o$4b8o$4b8o$4o8b4o$4o8b4o$4o8b4o$4o8b4o$4o8b4o$4o8b4o$4o8b4o$4o8b4o$4b8o$4b8o$4b8o$4b8o![[ THEME 0 AUTOSTART GPS 8 Z 16 T 1 T 1 Z 19.027 T 2 T 2 Z 22.627 T 3 T 3 Z 26.909 T 4 T 4 Z 32 T 5 T 5 Z 38.055 T 6 T 6 Z 45.255 T 7 T 7 Z 53.817 LOOP 8 ]]

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Re: Patterns that only work in 1 rule

Post by vivi » April 17th, 2022, 12:35 pm

patterns with this property are called endemic to a particular rule; this is more a question for the basic questions thread in general discussion (viewtopic.php?f=7&t=2036). there's lots of examples around, can't recall the smallest one in cgol but most (but definitely not all) engineered patterns and big spacedusty spaceships count.
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Re: Patterns that only work in 1 rule

Post by EvinZL » April 17th, 2022, 2:47 pm

There's a thread discussing this. The smallest example, in the linked post, is 78 cells in life:

Code: Select all

x = 34, y = 34, rule = B3/S23
bo27bo$bo26bobo$obo16b2o7bobo$bo17b2o6b2ob3o$bo31bo$bo25b2ob3o$bo25b2o
bo$obo$bo$bo4$25bo4b2o$24b3o3b2o$24bobo3$7bobo$2b2o3b3o$2b2o4bo7$3bob
2o$b3ob2o$o$b3ob2o6b2o$3bobo7b2o$3bobo$4bo!

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Re: Patterns that only work in 1 rule

Post by FractalFusion » April 17th, 2022, 5:53 pm

There is a wiki article "endemic" which I believe describes what you are describing. There are categories for endemic patterns both with respect to outer totalistic rules and with respect to isotropic rules.

For outer-totalistic, Figure eight on pentadecathlon is the smallest (24 cells) I could find.
For isotropic, 2 engine Cordership is the smallest (100 cells) I could find*, although likely there could be smaller.

*(excluding 17-glider reverse caber tosser which has a predecessor of no more than 17*5=85 cells)

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Re: Endemic periodic patterns and still lifes

Post by GUYTU6J » April 17th, 2022, 8:17 pm

Is LLS or any other program capable of finding and optimizing a still life with minimal anisotropic rule B/S012345678? See my first 2020 post above and also this handmade partial.

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Re: Patterns that only work in 1 rule

Post by dani » April 17th, 2022, 8:50 pm

FractalFusion wrote:
April 17th, 2022, 5:53 pm
*(excluding 17-glider reverse caber tosser which has a predecessor of no more than 17*5=85 cells)
I don't even think you need to go that far. A plain old BLSE/GPSE only works in CGoL. The lowest clean "phase" without non-interacting ash of a BLSE is 35 cells:

Code: Select all

x = 21, y = 28, rule = B3/S23
4b2o$4b2o19$bo$bo$obo11b2o$b3o9b2ob2o$b2o2b4o9b2o$bo7bo6bo3bo$2bo5bo8b
3o$2bo!
I wouldn't count a predecessor, which can get as low as 10 cells, because then you could just argue that the R-pentomino being endemic counts.

Interestingly, the raw Switch engine itself only works in B3/S23 +- S6e, but there are no elementary stable orbits like the block layer in the positive case.

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Re: Endemic periodic patterns and still lifes

Post by Macbi » April 17th, 2022, 9:57 pm

GUYTU6J wrote:
April 17th, 2022, 8:17 pm
Is LLS or any other program capable of finding and optimizing a still life with minimal anisotropic rule B/S012345678? See my first 2020 post above and also this handmade partial.
This is certainly something you could do with a SAT solver, but LLS isn't advanced enough to set up the search on its own. Also, De Bruijn tori are related.

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Re: Endemic periodic patterns and still lifes

Post by Macbi » April 19th, 2022, 2:57 am

GUYTU6J wrote:
April 17th, 2022, 8:17 pm
Is LLS or any other program capable of finding and optimizing a still life with minimal anisotropic rule B/S012345678? See my first 2020 post above and also this handmade partial.
Here is some code and a smallish solution. It seems that it might be out of reach to find an optimal solution for the 3 by 3 case at the moment.

Code: Select all

from pysat.card import CardEnc
import itertools
import subprocess
import sys

encoding = 8
clauses = []
number_of_variables = 0

target_width = 3
target_height = 3
width = 26
height = 26
max_pop = None

print(f'target_width = {target_width}')
print(f'target_height = {target_height}')
print(f'width = {width}')
print(f'height = {height}')
print(f'max_pop = {max_pop}')
print()

margin_width = target_width - 1
margin_height = target_height - 1
full_width = margin_width + width + margin_width
full_height = margin_height + height + margin_height

grid = [[None for x in range(full_width)] for y in range(full_height)]
target_variables = dict()

for x in range(full_width):
    for y in range(full_height):
        number_of_variables += 1
        grid[y][x] = number_of_variables
        if x < margin_width or full_width - x <= margin_width or y < margin_height or full_height - y <= margin_height:
            clauses.append([-number_of_variables])
            
for unrolled_target in itertools.product([-1,1],repeat=target_height*target_width):
    if all(cell==-1 for cell in unrolled_target):
        continue
    target = tuple(tuple(unrolled_target[target_width*y + x] for x in range(target_width)) for y in range(target_height))
    target_variables[target] = []
    for x in range(full_width - margin_width):
        for y in range(full_height - margin_height):
            number_of_variables += 1
            target_variables[target].append(number_of_variables)
            cell_variables = [target[y_offset][x_offset]*grid[y+y_offset][x+x_offset]
                              for x_offset in range(target_width)
                              for y_offset in range(target_height)]
            clauses.append([number_of_variables] + [-cell_variable for cell_variable in cell_variables])
            for cell_variable in cell_variables:
                clauses.append([-number_of_variables,cell_variable])
                
for target in target_variables:
    new_clauses = CardEnc.atleast(
        lits=target_variables[target],
        bound = 1,
        top_id = number_of_variables,
        encoding = encoding
    )
    number_of_variables = max(number_of_variables,new_clauses.nv)
    clauses += new_clauses.clauses
    
if max_pop is not None:
    new_clauses = CardEnc.atmost(
        lits = [grid[y][x] for x in range(full_width) for y in range(full_height)],
        bound = max_pop,
        top_id = number_of_variables,
        encoding = encoding
    )
    number_of_variables = max(number_of_variables,new_clauses.nv)
    clauses += new_clauses.clauses

cnf_string = "p cnf " + str(number_of_variables) + " " + str(len(clauses)) + "\n"
for clause in clauses:
    cnf_string += " ".join(str(literal) for literal in clause) + " 0\n"
print('Solving:')
solver_process = subprocess.Popen(
        [sys.path[0] + "/kissat"],
        stdout=subprocess.PIPE, stdin=subprocess.PIPE, stderr=subprocess.PIPE)
out, error = solver_process.communicate(bytes(cnf_string, 'utf-8'))

solution = (out.decode('ascii')).split("\ns ")[1].split("\nc")[0].split("\nv ") # Format kissat ouput
answers = [int(l) for l in " ".join(solution[1:]).split(" ")[:-1]] # looks like [-1, 2, 3,-4, 5, ...]
sat = solution[0] # "SATISFIABLE" or "UNSATISFIABLE"
print(sat)
if sat == "SATISFIABLE":
    for y in range(full_height):
        print(''.join('o' if grid[y][x] in answers else '.' for x in range(full_width)))

Code: Select all

x = 27, y = 27, rule = B/S012345678
3ob2ob7ob6obob2o$ob3o3b7o2bob2ob3obo$2o2bo2bo3bo9b3o2bo$b4obob2ob2obob
obo3b3o$bo4bo2bo3bob5ob3ob2o$ob7obo2b3o3b3ob4o$2ob2o2bob2ob5obob4ob2o$
2ob2obo3bob2obo4bobo3bo$9ob2o3bo3b2o2bob2o$o2bo2b2ob2o2b2o2b2o2b2o2bo$
2bobo2bob2o2b6obob2obo$o2b5o2b3ob4obo3bob2o$ob3ob2o4b2ob2obob2o2bo$o3b
ob2o2b2o2b2o3b2obobo$bo2bobo5bobob4obobob2o$2bo3bobo5b2o2bobo4bo$o4bo
4b2o2bob4o2bo3bo$2b2o2bo2bo3bo2b2obo2bo2bo$2obo5bob5o2bo2b2ob2o$bo3b3o
3bob2o3bob2obob2o$3o2bo2b2o2b2o2b2ob2ob2ob2o$bob5obo2bo5bob2o2b2o$2o2b
3obobob11o3bo$3b6ob2ob2o3b6ob2o$2obo19bo$b3o2b2obo2b2o2bo2bo2b2obo$2o
2b2obo2bob2ob2ob7o!

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Re: Endemic periodic patterns and still lifes

Post by Hdjensofjfnen » May 20th, 2022, 12:26 pm

Macbi wrote:
April 19th, 2022, 2:57 am
Here is some code and a smallish solution. It seems that it might be out of reach to find an optimal solution for the 3 by 3 case at the moment.
This site gives the following 33x17 (= 561) construction:

Code: Select all

x = 33, y = 17, rule = B/S012345678
6bob3o2bob3o2bob3o2bob3o$3bo2b6obo2b2ob2obobo4b2o$6bob3o2bob3o2bob3o2b
ob3o$3ob2o6bob2o2bo2bobob4o2b2o$6bob3o2bob3o2bob3o2bob3o$3bo2b6obo2b2o
b2obobo4b2o$2b2o3b3obob2ob5o3bobo2bo$o3bobo2b2ob2obobo4b2o3b6o$6obo3b
2obo3b2obo3b2obo3bo$3ob2o6bob2o2bo2bobob4o2b2o$obobo4bo2b4ob2o4bo2b4ob
2o$bo3b2obobo4b2o3b6obo2b2o$6obo3b2obo3b2obo3b2obo3bo$3ob2o6bob2o2bo2b
obob4o2b2o$b2o2bo2bo5b3obob2ob5o3bo$2ob5o2b3o6bob2o2bo2bobobo$6bob3o2b
ob3o2bob3o2bob3o!

Code: Select all

x = 5, y = 9, rule = B3-jqr/S01c2-in3
3bo$4bo$o2bo$2o2$2o$o2bo$4bo$3bo!

Code: Select all

x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!

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Re: Endemic periodic patterns and still lifes

Post by GUYTU6J » May 20th, 2022, 11:18 pm

Hdjensofjfnen wrote:
May 20th, 2022, 12:26 pm
This site gives the following 33x17 (= 561) construction...
I spent a while to figure out that the 256-cell pattern is meant to be put in a torus, and it is anisotropically endemic to B/S012345678.

Code: Select all

x = 32, y = 16, rule = B/S012345678:T32,16
6bob3o2bob3o2bob3o2bob3o$3bo2b6obo2b2ob2obobo4b2o$6bob3o2bob3o2bob3o2b
ob3o$3ob2o6bob2o2bo2bobob4o2bo$6bob3o2bob3o2bob3o2bob3o$3bo2b6obo2b2ob
2obobo4b2o$2b2o3b3obob2ob5o3bobo2bo$o3bobo2b2ob2obobo4b2o3b5o$6obo3b2o
bo3b2obo3b2obo$3ob2o6bob2o2bo2bobob4o2bo$obobo4bo2b4ob2o4bo2b4obo$bo3b
2obobo4b2o3b6obo2b2o$6obo3b2obo3b2obo3b2obo$3ob2o6bob2o2bo2bobob4o2bo$
b2o2bo2bo5b3obob2ob5o3bo$2ob5o2b3o6bob2o2bo2bobo!
Its invert seems to be a distinct solution.

Code: Select all

x = 32, y = 16, rule = B/S012345678:T32,16
6obo3b2obo3b2obo3b2obo$3ob2o6bob2o2bo2bobob4o2bo$6obo3b2obo3b2obo3b2ob
o$3bo2b6obo2b2ob2obobo4b2o$6obo3b2obo3b2obo3b2obo$3ob2o6bob2o2bo2bobob
4o2bo$2o2b3o3bobo2bo5b3obob2ob2o$b3obob2o2bo2bobob4o2b3o$6bob3o2bob3o
2bob3o2bob3o$3bo2b6obo2b2ob2obobo4b2o$bobob4ob2o4bo2b4ob2o4bo$ob3o2bob
ob4o2b3o6bob2o$6bob3o2bob3o2bob3o2bob3o$3bo2b6obo2b2ob2obobo4b2o$o2b2o
b2ob5o3bobo2bo5b3o$2bo5b2o3b6obo2b2ob2obobo!
To clarify the subtleties in my original question:
  • The pattern is finite, unlike a de Bruijn torus construction,
  • The pattern ignores the 2^8 birth (OFF center) conditions and considers only the 2^8 survival (ON center) conditions,
  • The pattern has no bounding box constraints, and
  • The pattern must contain exactly 2^8 ON cells, with one unique 3-by-3 neighbourhood each (anisotropically endemic to S012345678).
Based on the provided hexagonal solutions, a cluster-based approach may be favorable, that is, enumerating small clusters and finding valid combinations.
...
Maybe someone can try to contact the MindSports website owner and just ask for a solution?

affamatodidio
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Re: Endemic periodic patterns and still lifes

Post by affamatodidio » May 21st, 2022, 11:10 am

Even smaller endemic B/S012345678 pattern at 147 cells and 22 by 13 BB. Found by hand from other partials on this thread.

Code: Select all

x = 22, y = 13, rule = B/S012345678
bo3b2obo3b2obobob2o$obobo4b2o3b6obo$3bo2b4ob2o4bo2b2o$6bob2o2bo2bobob
3o$bo2b3obo3b2obo3b2o$o2b2ob2obobo4b2o3bo$b3obob2ob5o3bobo$6obo2b2ob2o
bobo$obobo2bob3o2bob3o2bo$6bob2o2bo2bobob3o$ob3o2bob3o2bob3o2bo$5o2bo
2b2ob2obobo$ob3o2bob3o2bob3o2bo!

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confocaloid
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Re: Endemic periodic patterns and still lifes

Post by confocaloid » May 21st, 2022, 9:04 pm

affamatodidio wrote:
May 21st, 2022, 11:10 am
Even smaller endemic B/S012345678 pattern at 147 cells and 22 by 13 BB. Found by hand from other partials on this thread.

Code: Select all

x = 22, y = 13, rule = B/S012345678
bo3b2obo3b2obobob2o$obobo4b2o3b6obo$3bo2b4ob2o4bo2b2o$6bob2o2bo2bobob
3o$bo2b3obo3b2obo3b2o$o2b2ob2obobo4b2o3bo$b3obob2ob5o3bobo$6obo2b2ob2o
bobo$obobo2bob3o2bob3o2bo$6bob2o2bo2bobob3o$ob3o2bob3o2bob3o2bo$5o2bo
2b2ob2obobo$ob3o2bob3o2bob3o2bo!
Isn't S7c optional?
127:1 B3/S234c User:Confocal/R (isotropic rules, incomplete)
Unlikely events happen.
My silence does not imply agreement, nor indifference. If I disagreed with something in the past, then please do not construe my silence as something that could change that.

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yujh
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Re: Endemic periodic patterns and still lifes

Post by yujh » May 21st, 2022, 9:48 pm

confocaloid wrote:
May 21st, 2022, 9:04 pm
affamatodidio wrote:
May 21st, 2022, 11:10 am
Even smaller endemic B/S012345678 pattern at 147 cells and 22 by 13 BB. Found by hand from other partials on this thread.

Code: Select all

x = 22, y = 13, rule = B/S012345678
bo3b2obo3b2obobob2o$obobo4b2o3b6obo$3bo2b4ob2o4bo2b2o$6bob2o2bo2bobob
3o$bo2b3obo3b2obo3b2o$o2b2ob2obobo4b2o3bo$b3obob2ob5o3bobo$6obo2b2ob2o
bobo$obobo2bob3o2bob3o2bo$6bob2o2bo2bobob3o$ob3o2bob3o2bob3o2bo$5o2bo
2b2ob2obobo$ob3o2bob3o2bob3o2bo!
Isn't S7c optional?
Yes. S7c seems to be missing.
Last edited by yujh on May 21st, 2022, 11:31 pm, edited 1 time in total.

affamatodidio
Posts: 212
Joined: September 14th, 2021, 7:45 pm

Re: Endemic periodic patterns and still lifes

Post by affamatodidio » May 21st, 2022, 10:23 pm

Code: Select all

x = 22, y = 13, rule = B/S012345678
bo3b2obo3b2obobob2o$obobo4b2o3b6obo$3bo2b4ob2o4bo2b2o$6bob2o2bo2bobob
3o$bo2b3obo3b2obo3b2o$ob3ob2obobo4b2o3bo$b3obob2ob5o3bobo$6obo2b2ob2o
bobo$obobo2bob3o2bob3o2bo$6bob2o2bo2bobob3o$ob3o2bob3o2bob3o2bo$6obo2b
2ob2obobo$ob3o2bob3o2bob3o2bo!

fixed

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yujh
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Re: Endemic periodic patterns and still lifes

Post by yujh » May 21st, 2022, 10:59 pm

affamatodidio wrote:
May 21st, 2022, 10:23 pm

Code: Select all

x = 22, y = 13, rule = B/S012345678
bo3b2obo3b2obobob2o$obobo4b2o3b6obo$3bo2b4ob2o4bo2b2o$6bob2o2bo2bobob
3o$bo2b3obo3b2obo3b2o$ob3ob2obobo4b2o3bo$b3obob2ob5o3bobo$6obo2b2ob2o
bobo$obobo2bob3o2bob3o2bo$6bob2o2bo2bobob3o$ob3o2bob3o2bob3o2bo$6obo2b
2ob2obobo$ob3o2bob3o2bob3o2bo!

fixed
slight reductions all over the place:

Code: Select all

 x = 22, y = 13, rule = B/S012345678
5bo2bo8bob2o$4bo4b2o5b4obo$3bo2b4ob2o4bo2b2o$6bob2o2bo4bob3o$bo2b3obo
3b2o5b2o$2b3ob2obobo4b2o3bo$b3obob2ob5o3bobo$b5obo2b2ob2obobo$obobo2bo
b3o2bob3o$6bob2o2bo2bobob2o$ob3o2bob3o2bob3o$2b4obo2b2ob2obobo$2b3o2bo
6bob3o!
(pretty easy to spot, i should have missed a lot of other stuff)

fluffykitty
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Re: Endemic periodic patterns and still lifes

Post by fluffykitty » May 22nd, 2022, 2:07 am

yujh wrote:
May 21st, 2022, 10:59 pm
slight reductions all over the place:

Code: Select all

 x = 22, y = 13, rule = B/S012345678
5bo2bo8bob2o$4bo4b2o5b4obo$3bo2b4ob2o4bo2b2o$6bob2o2bo4bob3o$bo2b3obo
3b2o5b2o$2b3ob2obobo4b2o3bo$b3obob2ob5o3bobo$b5obo2b2ob2obobo$obobo2bo
b3o2bob3o$6bob2o2bo2bobob2o$ob3o2bob3o2bob3o$2b4obo2b2ob2obobo$2b3o2bo
6bob3o!
(pretty easy to spot, i should have missed a lot of other stuff)
Your pattern has an extra space at the start. Also, more reduction:

Code: Select all

x = 17, y = 12, rule = B/S01234567c8
12bob2o$b3o3b2o2b4obo$2bob4ob2obo2b2o$o3bob2o2bobob3o$2b3obo3bobob2o$b
2ob2obobo$2obob2ob5ob3o$4obo2b2ob2obobo$4obob3o2bob3o$3obob2o2bo2bobo$
bo3bob3o2bob3o$8b2obo2bobo!
And a verification script (Python 2, probably works in 3 if you change the xrange to range but idk):

Code: Select all

import golly as g
rules=["S12345678","S01234567"]
things={1:"ce",2:"cekain",3:"cekainyqjr",4:"cekainyqjrtwz"}
things[5]=things[3]
things[6]=things[2]
things[7]=things[1]
for i in xrange(1,8):
	for j in things[i]:
		x="S012345678".replace(str(i),str(i)+"-"+j)
		rules.append(x)
for i in rules:
	g.reset()
	p=g.getpop()
	g.setrule(i)
	g.step()
	if g.getpop()==p:
		1/0
g.reset()
Edit: Better pattern:

Code: Select all

x = 16, y = 9, rule = B/S01234567c8
2bob4obo2b3o$o3bob2obo3b3o$o2b2obobobo3b2o$b2ob2obobo3b2o$bobobo2b4obo
bo$4obo2b2obob3o$4obob3o2bobo$3ob4o2bo2b3o$bobobo5bo!

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yujh
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Re: Endemic periodic patterns and still lifes

Post by yujh » May 22nd, 2022, 9:21 am

fluffykitty wrote:
May 22nd, 2022, 2:07 am
snip
except you forgot birth transitions. i also have no idea how to write a script, i just check catagolue for that.
Edit:123 cells

Code: Select all

x = 22, y = 13, rule = B/S012345678
5bo2bo8bob2o$4bo4b2o5b4obo$3bo2b4o4b2obo2b2o$6bob2o5bobob3o$bo2b3obo10b
2o$2b3ob2obobo4b2o3bo$b3obob2ob5o3bobo$b5obo2b2ob2obobo$obobo2bob3o2b
ob3o$6bob2o2bo2bobob2o$ob3o2bob3o2bob3o$2b4obo2b2ob2obobo$2b3o2bo6bob
3o!
122:

Code: Select all

x = 27, y = 22, rule = B/S012345678
4$7bo2bo8bob2o$6bo4b2o5b4obo$5bo2b4o4b2obo2b2o$8bob2o5bobob3o$3bo2b3o
bo10b2o$4b3ob2obobo4b2o3bo$3b3obob2ob5o3bobo$3b5o4b2ob2obobo$2bobobo2b
ob3o2bob3o$8bob2o2bo2bobob2o$2bob3o2bob3o2bob3o$4b4obo2b2ob2obobo$4b3o
2bo6bob3o!

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