Small Spacefillers

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
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Rocknlol
Posts: 125
Joined: April 15th, 2012, 9:06 am

Small Spacefillers

Post by Rocknlol » November 17th, 2021, 9:25 pm

I've been conducting a non-exhaustive, targeted search for low-population/small-bounding box Max variants over the last few days using LLS. Below are the lowest-population variants I could find for each of their respective bounding boxes:

151-cell, 27x23:

Code: Select all

x = 27, y = 23, rule = B3/S23
17b2o$17bob2o$12b3o3b2obob2o$11bo2b3o2bobobo$4b2o4bo3b2o5b3o$4bo5bo5bo
bobo2bo$b4o7bo5bo$bo7bobo9bo2bobo$3bo2b2ob3ob2o6bobobo$o4bo3bobobo$bob
o3bobo2bo2b2o7bo$2bob2o2bo2bobobo2bo2b2obo$2bo7b2o2bo2bobo3bobo$13bobo
bo3bo4bo$bobobo6b2ob3ob2o2bo$obo2bo9bobo7bo$8bo5bo7b4o$3bo2bobobo5bo5b
o$3b3o5b2o3bo4b2o$3bobobo2b3o2bo$2b2obob2o3b3o$6b2obo$8b2o!
155-cell, 25x23:

Code: Select all

x = 25, y = 23, rule = B3/S23
16b2o$11bo5b2o3b2o$4b2o6b2o4b2o$2bo5bobo2b4ob3o2bo$3b3o3b2o2bo8bo$15bo
3bo3bo$4o7bo3bobobobo$o2bo4b3o10bobo$6bobobob2o6bo2b2o$4bobobo3bobo7bo
$3obo2b2ob2o3bo$bobo4bobobobobo4bobo$9bo3b2ob2o2bob3o$2bo7bobo3bobobo$
2o2bo6b2obobobo$bobo10b3o4bo2bo$3bobobobo3bo7b4o$bo3bo3bo$2bo8bo2b2o3b
3o$bo2b3ob4o2bobo5bo$5b2o4b2o6b2o$b2o3b2o5bo$7b2o!
161-cell, 25x21:

Code: Select all

x = 25, y = 21, rule = B3/S23
11bo2bob3obobo$16bobo2b2o$2bo6b3ob3obo4bobo$14bobo2bobo2bo$3b3o3bo11bo
$2o8b2o4b3o5bo$obo3bobo7bobobo$5b2o4b2o6bo2b2o$2bo3b3o3bo2b2o4bob2o$2b
ob2o2b3obobo2bob3ob2o$bo2bo5bobobo5bo2bo$2ob3obo2bobob3o2b2obo$2obo4b
2o2bo3b3o3bo$b2o2bo6b2o4b2o$4bobobo7bobo3bobo$o5b3o4b2o8b2o$3bo11bo3b
3o$o2bobo2bobo$obo4bob3ob3o6bo$2b2o2bobo$2bobob3obo2bo!
189-cell, 23x23

Code: Select all

x = 23, y = 23, rule = B3/S23
14bobobobo$b2o13b2o3b2o$4bo2bo2b2o5bo$b2obo4bo2b2obobo2bobo$4b2obobo2b
o2bo2b2o$bo2b3o6bobo3bob2o$o2bo2bob2o2b2o2b2obo2bo$o4b2o2bo5bobo2bobo$
3o4bobob2o2b2o3bobo$5b3o6bo3b2o$ob3o2bob2o4bo2b2ob2o$obo5b2obob2o5bobo
$2ob2o2bo4b2obo2b3obo$3b2o3bo6b3o$obo3b2o2b2obobo4b3o$obo2bobo5bo2b2o
4bo$o2bob2o2b2o2b2obo2bo2bo$2obo3bobo6b3o2bo$3b2o2bo2bo2bobob2o$obo2bo
bob2o2bo4bob2o$5bo5b2o2bo2bo$2o3b2o13b2o$2bobobobo!

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iNoMed
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Posts: 607
Joined: August 29th, 2020, 3:05 pm
Location: Scotland

Re: Small Spacefillers

Post by iNoMed » December 29th, 2022, 7:37 am

Here's a 135-cell Max variant based off the 151-cell Max predecessor from this thread:

Code: Select all

x = 27, y = 25, rule = B3/S23
19b3o$18bo2bo$18bo2bo$12b3o3bo3bo$11bo2bo2bo4bo$4b2o4bo3bo2bo$4bo5bo
10bo$b4o7bo4b3o$bo7bobo9bo2bobo$3bo2b2ob3ob2o6bobobo$o4bo3bobobo$bobo
3bobo2bo2b2o7bo$2bob2o2bo2bobobo2bo2b2obo$2bo7b2o2bo2bobo3bobo$13bobob
o3bo4bo$bobobo6b2ob3ob2o2bo$obo2bo9bobo7bo$7b3o4bo7b4o$5bo10bo5bo$9bo
2bo3bo4b2o$4bo4bo2bo2bo$4bo3bo3b3o$5bo2bo$5bo2bo$5b3o!
Edit: 131 cells:

Code: Select all

x = 27, y = 25, rule = B3/S23
19b3o$18bo2bo$18bo2bo$12b3o3bo3bo$11bo2bo2bo4bo$4b2o4bo3bo2bo$4bo5bo$b
4o7bo3bobo$bo7bobo9bo2bobo$3bo2b2ob3ob2o6bobobo$o4bo3bobobo$bobo3bobo
2bo2b2o7bo$2bob2o2bo2bobobo2bo2b2obo$2bo7b2o2bo2bobo3bobo$13bobobo3bo
4bo$bobobo6b2ob3ob2o2bo$obo2bo9bobo7bo$8bobo3bo7b4o$16bo5bo$9bo2bo3bo
4b2o$4bo4bo2bo2bo$4bo3bo3b3o$5bo2bo$5bo2bo$5b3o!
Edit 2: 127 cells at the cost of being weird:

Code: Select all

x = 33, y = 23, rule = B3/S23
23b3o$22bo2bo$22bo2bo$16b3o3bo3bo$15bo2bo2bo3bo4bo$8b2o4bo3bo2bo6bo3bo
$8bo5bo11bo3bo$5b4o7bo3bobo3bobo$5bo7bobo14bo$7bo2b2ob3ob2o7bo$4bo4bo
3bobobo2bo2b2obo$5bobo3bobo2bo2bobo3bobo$6bob2o2bo2bobobo3bo4bo$6bo7b
2ob3ob2o2bo$2bo14bobo7bo$4bobo3bobo3bo7b4o$2bo3bo11bo5bo$o3bo6bo2bo3bo
4b2o$2bo4bo3bo2bo2bo$6bo3bo3b3o$7bo2bo$7bo2bo$7b3o!
Edit 3: Max 127, now less ugly:

Code: Select all

x = 27, y = 23, rule = B3/S23
20b3o$19bo2bo$19bo2bo$13b3o3bo3bo$12bo2bo2bo3bo$5b2o4bo3bo2bo6bo$5bo5b
o10bo3bo$2b4o7bo3bobo2b5o$2bo7bobo11bo$4bo2b2ob3ob2o$6bo3bobobo2bo2b2o
bo$b2obo3bobo2bo2bobo3bob2o$3bob2o2bo2bobobo3bo$11b2ob3ob2o2bo$2bo11bo
bo7bo$5o2bobo3bo7b4o$o3bo10bo5bo$bo6bo2bo3bo4b2o$4bo3bo2bo2bo$3bo3bo3b
3o$4bo2bo$4bo2bo$4b3o!

Code: Select all

x = 35, y = 5, rule = B3/S23
4b2o3b2o3bo3b2ob2o3b2ob2o$2o2bobo3bo2bobobobobobobobobobo$obobo2bo2bob
o2bobo2bo2bobo3bobo$2bobo3bobobobo2bo5bobo3bobob2o$b2ob2o3b2ob2o3b2o3b
2ob2o3b2ob2o!

Rocknlol
Posts: 125
Joined: April 15th, 2012, 9:06 am

Re: Small Spacefillers

Post by Rocknlol » December 31st, 2022, 5:46 am

Improvements to both population and bounding box from swapping out the above p4 support with HWSSs and running predecessor searches:

112-cell, 25x23:

Code: Select all

x = 25, y = 23, rule = B3/S23
19b3o$19bo2bo$12b2o5bo$10bo2b2o4bo$11bo2bo4bo$o8bo4bo4bo$3bo7bo8bo$b2o
2bo3bobobo9bo$b2o3bo2b3obo8bo$o2b2o3bo2bo2bobo3bo2b2o$2bo3bo5bo3bo3bo$
2bobo3bobo3bobo3bobo$4bo3bo3bo5bo3bo$2o2bo3bobo2bo2bo3b2o2bo$2bo8bob3o
2bo3b2o$bo9bobobo3bo2b2o$4bo8bo7bo$5bo4bo4bo8bo$5bo4bo2bo$5bo4b2o2bo$
5bo5b2o$2bo2bo$3b3o!
115-cell, 23x23:

Code: Select all

x = 23, y = 23, rule = B3/S23
18b3o$18bo2bo$12bo5bo$11b3o4bo$10b2obo4bo$o8b2o2bo4bo$bo9bo7bo$o2bo4bo
bo$2o3bo2b2o3bo7bo$3obo3bo2b2o6b4o$bo3b2obo4b2o7bo$3bob2obob3obob2obo$
o7b2o4bob2o3bo$4o6b2o2bo3bob3o$bo7bo3b2o2bo3b2o$12bobo4bo2bo$3bo7bo9bo
$4bo4bo2b2o8bo$4bo4bob2o$4bo4b3o$4bo5bo$bo2bo$2b3o!
134-cell, 21x21:

Code: Select all

x = 21, y = 21, rule = B3/S23
11b2o4b3o$2bo13bo2bo$9bobo7bo$b2o10bo3bo2bo$2ob2obo2b2o2bo4bo$3bo2bo2b
o3bo2bo$o8b3o3b2o3bo$o4b2o3b2o3bo2bo$2obobobo3bo2bo4b2o$bo3bob3obobo2b
2o2bo$3o4bo5bo4b3o$o2b2o2bobob3obo3bo$2o4bo2bo3bobobob2o$2bo2bo3b2o3b
2o4bo$o3b2o3b3o8bo$4bo2bo3bo2bo2bo$2bo4bo2b2o2bob2ob2o$o2bo3bo10b2o$bo
7bobo$bo2bo13bo$b3o4b2o!
EDIT: Also found a 110-cell, 27x23 spacefiller:

Code: Select all

x = 27, y = 23, rule = B3/S23
20b3o$14bo5bo2bo$20bo$12bob2o4bo$12b4o4bo$12b2o3bo2bo$2b2o7bo9bo$2bo6b
o3bo9bo$4b2o3bo3bo3b2o5bo$2o4b2obo3bo10bo$4bo6bo3bobobob3o$2bob2o2bo2b
o3bo2bo2b2obo$3b3obobobo3bo6bo$2bo10bo3bob2o4b2o$2bo5b2o3bo3bo3b2o$3bo
9bo3bo6bo$5bo9bo7b2o$6bo2bo3b2o$6bo4b4o$6bo4b2obo$6bo$3bo2bo5bo$4b3o!

Naszvadi
Posts: 1244
Joined: May 7th, 2016, 8:53 am
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Re: Small Spacefillers

Post by Naszvadi » January 6th, 2023, 11:05 am

Rocknlol wrote:
December 31st, 2022, 5:46 am
Improvements to both population and bounding box from swapping out the above p4 support with HWSSs and running predecessor searches:
...

EDIT: Also found a 110-cell, 27x23 spacefiller:

Code: Select all

x = 27, y = 23, rule = B3/S23
20b3o$14bo5bo2bo$20bo$12bob2o4bo$12b4o4bo$12b2o3bo2bo$2b2o7bo9bo$2bo6b
o3bo9bo$4b2o3bo3bo3b2o5bo$2o4b2obo3bo10bo$4bo6bo3bobobob3o$2bob2o2bo2b
o3bo2bo2b2obo$3b3obobobo3bo6bo$2bo10bo3bob2o4b2o$2bo5b2o3bo3bo3b2o$3bo
9bo3bo6bo$5bo9bo7b2o$6bo2bo3b2o$6bo4b4o$6bo4b2obo$6bo$3bo2bo5bo$4b3o!
I can confirm that the last 110 cell spacefiller does not have a C2-symmetric father with at most 107 cells in a slightly bigger (29x25) bounding box:

Code: Select all

Time used: 7984.3 secs.  Memory used: 426.0 Mb.
+10953265: mip =     not found yet >=   1.080000000e+02        (229985; 28171)
Modified the life_goe.mod included in the GLPK examples, originally it looks for a father pattern for a given one.
Added a constraint to force C2 symmetry and an objective function that minimizes the father's population.

Rocknlol
Posts: 125
Joined: April 15th, 2012, 9:06 am

Re: Small Spacefillers

Post by Rocknlol » January 8th, 2023, 6:17 pm

107-cell 25x23:

Code: Select all

x = 25, y = 23, rule = B3/S23
19b3o$13bo5bo2bo$13bo5bo$11bo2bo4bo$11b4o4bo$3bo7b2o3bo2bo$o9bo9bo$b2o
5bo3bo10bo$4bo3bo3bo9bo$2obob2obo3bo3b2o4bo$4bo5bo3b2o4bo3bo$2bob2o2bo
3bo3bo2b2obo$o3bo4b2o3bo5bo$2bo4b2o3bo3bob2obob2o$2bo9bo3bo3bo$bo10bo
3bo5b2o$4bo9bo9bo$5bo2bo3b2o7bo$5bo4b4o$5bo4bo2bo$5bo5bo$2bo2bo5bo$3b
3o!
113-cell 23x23:

Code: Select all

x = 23, y = 23, rule = B3/S23
18b3o$10bo7bo2bo$12bo5bo$12b2o4bo$9b3obo4bo$3bo6b2o3bo2bo$bo9bo7bo$3o
6bo11bo$o3bob2obo3bo5bobo$4b2o4bob3o4bo2bo$bo2bob2o9b2o2b2o$2o6bo2bo2b
o6b2o$2o2b2o9b2obo2bo$o2bo4b3obo4b2o$bobo5bo3bob2obo3bo$bo11bo6b3o$3bo
7bo9bo$4bo2bo3b2o6bo$4bo4bob3o$4bo4b2o$4bo5bo$bo2bo7bo$2b3o!
124-cell 21x21:

Code: Select all

x = 21, y = 21, rule = B3/S23
11bo5b3o$2bo8bobo2bo2bo$3bo7bobo5bo$4bobo4bobo4bobo$2bo2bo3bo7bo$obo2b
o4bo2bo5bo$o4bo3b2o8bo$o3bobo4b2o4bob2o$bo4bo3bo9bo$2b2o3bo3bobo2bo2b
2o$4obob3ob3obob4o$2o2bo2bobo3bo3b2o$o9bo3bo4bo$2obo4b2o4bobo3bo$bo8b
2o3bo4bo$bo5bo2bo4bo2bobo$3bo7bo3bo2bo$obo4bobo4bobo$bo5bobo7bo$bo2bo
2bobo8bo$b3o5bo!
142-cell 21x19 (a new bounding box):

Code: Select all

x = 21, y = 19, rule = B3/S23
8bo2b3o3b3o$bo5bo3b2o4bo2bo$ob3ob3o8bo$2bo2b2o3b3o3bobo$o4bo3b2obob2o
2bo$2obo2bo7b2ob3o$2bo4bo3b4obo2bo$11bobo$3b4o2bo2bobo2b2obo$4o4bo3bo
4b4o$ob2o2bobo2bo2b4o$7bobo$bo2bob4o3bo4bo$b3ob2o7bo2bob2o$2bo2b2obob
2o3bo4bo$2bobo3b3o3b2o2bo$3bo8b3ob3obo$o2bo4b2o3bo5bo$b3o3b3o2bo!

On a whim I've also looked for spacefillers where every cell in the universe is alive at some point (as opposed to all but finitely many.)

139-cell 23x21:

Code: Select all

x = 23, y = 21, rule = LifeHistory
14.A3.3A$2.A7.A2.A3.A2.A$12.A.2A4.A$2.2A.A4.A9.A$A.A.A.A.3A4.A3.A2.A$
14.2A3.A$.A.2A4.A.A2.2A.A4.A$A3.A6.3A.A$.A.A.A.A.3A6.A.2A$2.A2.A.A3.A
.A.2A.A2.A$.3A5.A.A.A5.3A$.A2.A.2A.A.A3.A.A2.A$.2A.A6.3A.A.A.A.A$7.A.
3A6.A3.A$A4.A.2A2.A.A4.2A.A$3.A3.2A$A2.A3.A4.3A.A.A.A.A$2.A9.A4.A.2A$
2.A4.2A.A$2.A2.A3.A2.A7.A$2.3A3.A!
153-cell 21x21:

Code: Select all

x = 21, y = 21, rule = LifeHistory
11.A5.3A$.2A13.A2.A$4.A4.2A.A7.A$.A4.A.A3.A4.A.A$2A.A2.3A3.A.A2.2A$3.
2A5.A2.A4.A$A4.2A.A.A2.2A.3A.A$A5.A.A.A.A3.A.A$2A.A.3A.3A.A3.A.2A$2.A
2.2A3.A4.A4.A$3A.A3.A.A.A3.A.3A$A4.A4.A3.2A2.A$2A.A3.A.3A.3A.A.2A$2.A
.A3.A.A.A.A5.A$A.3A.2A2.A.A.2A4.A$2.A4.A2.A5.2A$2.2A2.A.A3.3A2.A.2A$.
A.A4.A3.A.A4.A$A7.A.2A4.A$.A2.A13.2A$.3A5.A!

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