"Glass tile oscillators" + natural spaceships [CA collection thread]
Posted: December 6th, 2024, 11:05 am
Definition: by definition, a glass tile oscillator is a statorless oscillator whose envelope is a solid rectangle without any "holes" or "defects".
(Notes:
The envelope of an oscillator consists of all cells that are alive in at least one phase.
Find the envelope of an oscillator. Find the bounding box of the envelope. If every cell within the bounding box of the envelope belongs to the rotor of the oscillator, then it's a "glass tile oscillator".)
This forum thread is a collection thread, intended for cellular automata with all of the following properties:
The following properties are optional:
Here is an example CA from an earlier post, with at least three "glass tile oscillators" with periods above 9, and with at least three naturally occurring spaceships:
(There are also known infinite families, such as the one shown below. I'm more curious about "nonadjustable" examples that do not appear to belong in any infinite family.)
Several open problems:
Here are several more known examples:
(Notes:
The envelope of an oscillator consists of all cells that are alive in at least one phase.
Find the envelope of an oscillator. Find the bounding box of the envelope. If every cell within the bounding box of the envelope belongs to the rotor of the oscillator, then it's a "glass tile oscillator".)
This forum thread is a collection thread, intended for cellular automata with all of the following properties:
- There should be at least one "glass tile oscillator" with period above 9.
- There should be at least one naturally occurring spaceship.
- Two cellstates only.
The following properties are optional:
- It should be possible to search the CA using apgsearch, without major slowdown or major memory consumption.
Here is an example CA from an earlier post, with at least three "glass tile oscillators" with periods above 9, and with at least three naturally occurring spaceships:
Code: Select all
#C Statorless oscillators with solid rectangular envelopes:
#C p12 (12-by-3), p46 (9-by-8), p10 (6-by-4), p6 (6-by-3)
#C Naturally occurring spaceships:
#C p9 diagonal 2c/9, p6 orthogonal c/3, p4 orthogonal c/4
x = 28, y = 25, rule = B34cijn58/S1268
3b2o2b2o$obo6bobo12b3o$3b2o2b2o18bo$25bobo$27bo2$4b4o$3b6o$3bo4bo$3bob
2obo2$24bobo$24b2o$25bo$26bo2$3bo$3bobobo$4bobobo$8bo2$25bo$5b2o17b2o$
3bob2obo16bo$3b2o2b2o!
#C [[ MAXGRIDSIZE 9 GRID THEME Catagolue ]]
Code: Select all
x = 80, y = 22, rule = B2e3-c/S2-cn3-cr:T100,35
o2bo$4o$6bo21bo19bo17bo$7bo21bo19bo17bo$8bo21bo19bo17bo$9bo21bo19bo17b
o$10bo21bo19bo17bo$11bo21bo19bo17bo$12bo21bo19bo17bo$13bo21bo19bo17bo$
14bo21bo19bo17bo$15bo21bo19bo17bo$16bo21bo19bo17bo$17bo21bo19bo17bo$
18bo21bo19bo17bo$19bo21bo19bo17bo$20bo21bo19bo$21bo21bo19bo$22bo21bo$
23bo21bo$24bo$25bo!
#C [[ GRID THEME Catagolue ]]
- Find an example CA with additional property that multiple copies of a "glass tile oscillator" can indeed be used as tiles, with precisely one column of permanently-dead cells between horizontally adjacent tiles, and with precisely one row of permanently-dead cells between vertically adjacent tiles. (In other words, it should be possible to pack the tiles as densely as one could hope for.)
- In addition to already stated properties: every such densely-packed finite array of translated copies of a "glass tile oscillator" should be constructible by colliding common spaceships.
- In addition to already stated properties: it should be possible (at least in principle) to use arrays of "glass tile oscillator" tiles as R/W memory, via presence or absence of individual tiles in the array. There should be sufficient technology to be able to "read from" and "write to" such densely-packed arrays of tiles.
- Can all of this be achieved with strictly volatile "glass tile oscillator" tiles?
Here are several more known examples:
Code: Select all
#C p104 statorless oscillator with a rectangular (15-by-3) envelope,
#C p70 orthogonal 2c/35 spaceship,
#C found by LaundryPizza03 in the Catagolue census:
#C https://catagolue.hatsya.com/census/b2ei3aij4ei5ys01e3any4ct5i/C1
x = 10, y = 13, rule = B2ei3aij4ei5y/S01e3any4ct5i:T52,39
5bo$2bo2bo3bo$5bo8$4bo$o3bobo2bo$4bo!
#C [[ GRID THEME Catagolue ]]
Code: Select all
#C p22 statorless oscillator with a rectangular (7-by-6) envelope,
#C p16 orthogonal c/8 spaceship,
#C found by Harfordson Parker-Cole in the Catagolue census:
#C https://catagolue.hatsya.com/census/b2kn3aceir4aknwz5cnqry6ai7e8s2-c3aejqr4cen5aeqr6ci8/C1
x = 8, y = 13, rule = B2kn3aceir4aknwz5cnqry6ai7e8/S2-c3aejqr4cen5aeqr6ci8:T44,44
3b2o$bo2b2o$b2o2bo$2b2o6$b4o$5o$3b5o$5b3o!
#C [[ GRID THEME Catagolue ]]
Code: Select all
#C p12 statorless oscillator with a rectangular (7-by-6) envelope,
#C three orthogonal c/2 spaceships (two p6 and one p2),
#C two p4 diagonal c/4 spaceships,
#C found by Yoel Matveyev in the Catagolue census:
#C https://catagolue.hatsya.com/census/b3-qr4k5ai6ck78s2-ck3-ai4-k5qr678/C1
x = 36, y = 30, rule = B3-qr4k5ai6ck78/S2-ck3-ai4-k5qr678:T80,80
3bo18b4o$b2ob2o15b6o6bo$bo3bo14bob4obo6b2o$b5o14b8o5b2o$20bob4obo5b2o$
21bob2obo5b4o$22b4o7$22bobo$21bobo$21b5o$20bob4o$21b4o$20b4o$21b2o$8bo
$7bo$7b3o3$o$obo$2obo$2bo$2b3o!
#C [[ GRID THEME Catagolue ]]
Code: Select all
#C p30 statorless oscillator with a rectangular (6-by-6) envelope,
#C p12 diagonal c/12 spaceship,
#C p205 orthogonal 4c/205 spaceship,
#C p17 orthogonal c/17 spaceship,
#C p12 orthogonal c/6 spaceship,
#C p8 orthogonal c/8 spaceship,
#C p5 orthogonal c/5 spaceship,
#C p4 orthogonal c/4 spaceship,
#C found by FWKnightship in the Catagolue census:
#C https://catagolue.hatsya.com/census/b2cei3akqy4akw5iy6ik7c8s01c2eik3-aq4aceirwy5eikny6cei8/C1
x = 22, y = 71, rule = B2cei3akqy4akw5iy6ik7c8/S01c2eik3-aq4aceirwy5eikny6cei8:T68,100
o12$8bobo$9bo$8bo8$18b3o$18bobo$18bobo$15bobo$15bobo$15b3o5$16bo$15bo$
16bo4$15b4o$15b2ob2obo$15b4o4$19bo$15bo4bo$19bo5$15bo$15b2o$15bobo$15b
o2bo$15bobo$15b2o$15bo5$16bobo$15b3o$16bobo4$17bo$15bo$17bo!
#C [[ GRID THEME Catagolue ]]
Code: Select all
#C p32 statorless oscillator with a rectangular (7-by-6) envelope,
#C p1132 diagonal c/283 spaceship, p27 (2,1)c/27 knightship, p3 diagonal c/3 spaceship,
#C found by LaundryPizza03 in the Catagolue census:
#C https://catagolue.hatsya.com/census/b2ikn3aikry4cej5ack6an7cs12aen3aeqry4-ciqz5ak6an7e8/C1
x = 65, y = 6, rule = B2ikn3aikry4cej5ack6an7c/S12aen3aeqry4-ciqz5ak6an7e8
20b2o17bo19bo$2b3o14b2o19bo19bo$3b2o57b3o$2o17bo23b2o17b3o$3o39bo19b2o
$40bob3o!
#C [[ MAXGRIDSIZE 9 GRID THEME Catagolue ]]