OCA:Diamoeba

Diamoeba
x=64, y = 64, rule = B35678/S5678 ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE2 RANDSEED 1729 THUMBLAUNCH THUMBNAIL THUMBSIZE 2 GRID ZOOM 6 WIDTH 600 HEIGHT 600 LABEL 90 -20 2 "#G" AUTOSTART PAUSE 2 GPS 8 LOOP 256 ]] LifeViewer-generated pseudorandom soup
View static image
Rulestring	5678/35678 B35678/S5678
Rule integer	246248
Character	Stable
Black/white reversal	B45678/S4678

Diamoeba is a Life-like cellular automaton where cells are born if they have 3, 5, 6, 7, or 8 neighbors, and survive if they have 5-8 neighbors. Like in 2×2, patterns made of blocks will permanently remain made of blocks.

Diamoeba is known for its dynamics. Small random soups often dissolve into vacuum or small oscillators while larger soups often generate large oscillating diamonds.

There are no still lifes in Diamoba. Consider for example the leftmost living cell in the top row of a hypothetical Diamoeba still life; call this cell "TL". To survive into the next generation, cell TL must have at least five neighbors. TL is in the top row, so its five neighbors must be the three neighbors below it, plus the two in its own row, to the left and right. A cell to the left of TL contradicts the initial assumption, so no still lifes can exist.

Known objects

Oscillators

There are many oscillators in Diamoeba, although all of the known ones are of even period until 2023. Below is a collection of the smallest known oscillators (by cell count) from periods 2 to 14.

x = 66, y = 10, rule = B35678/S5678 2bo8bo8bobobobo5b4o5bobobobo3bobo7bobo$obo7bob3o7b6o4b4o4b6o7bobo7bobo $obo8b4o5b6o4b8o4b6o2b4o6b4o$2bo8b4o6bobobobo4b4o4bob3obo5b3o7b3o$11b 4o8bobo4bob4obo7bo5b5o5b3o$32bo18b5o6b4o$52b3o6b3o$50b4o8b3o$53bobo4bo bo$51bobo8bobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

(click above to open LifeViewer)

The only known odd period oscillator had been discovered on June 10, 2023. This one has period 35:

x = 16, y = 16, rule = B35678/S5678 5bob3o$4b8o$4b8o$3b10o$b14o$b15o$7o2b6o$6o4b6o$6o4b6o$b6o2b7o$15o$b14o $3b10o$4b8o$4b8o$6b3obo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

(click above to open LifeViewer) Catagolue: here

Spaceships

speed	period	first known	discoverer	minimal known	discoverer
c/7	7	144P7H1V0	David Eppstein, 1999	112P7H1V0	cyl, 2023
	14			204P14H2V0	Saka
c/9	9	548P9H1V0	Josh Ball, 2015	162P9H1V0	djgjs, 2015
c/16	16			105P16H1V0	Dongook Lee, 2015

All known spaceships are orthogonal and no spaceship faster than c/7 orthogonal is currently known. Below is a display of the smallest known spaceships (by population) of each known speed.

x = 47, y = 22, rule = B35678/S5678 6b2o14bo2bo14bobo$3bob4obo10b6o11bobobobo$3b8o10b6o11b7o$3b8o7b12o7b9o$5b4o10b10o7b11o$5b4o10b10o7b11o$6b2o11b10o7b11o$5b4o10b10o7b11o$6b2o11b10o7b11o$4b6o10b8o8b11o$6b2o11b10o7b11o$5b4o11b8o9bobobobobo$6b2o10b12o11bo$3b8o9b8o$2bo3b2o3bo7b10o$ob3o4b3obo7b6o$b12o7b8o$5o4b5o7b6o$b12o7bob4obo$b4o4b4o9b4o$3b8o$5bo2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] [[ THUMBSIZE 2 ZOOM 12 WIDTH 784 HEIGHT 560 ]]

From left to right: c/7, c/9, c/16 (click above to open LifeViewer)

Infinite growth

There are four known infinite growth patterns so far, a c/7 orthogonal wickstretcher found by David Bell, a quarter-spacefiller also found by David Bell of the same speed, a spacefiller yet again by David Bell based on a spaceship, and a c/7 orthogonal wickstretcher found by Arie Paap.

x = 62, y = 138, rule = B35678/S5678 3b2o12b2o$bob2obo8bob2obo13bo11bo3bo3bobob3o$8o6b8o9b2obobobobobobobob obobobobob2o$b6o8b6o10b30o$8o6b8o9b31o$2b4o10b4o11b31o$8o8b4o11b30o$2b 4o25b2obobobobobobobobobobobobob2o$b6o8b6o13bo11bo3bo3bobob3o$2b4o$8o 9b2o$2b4o$b6o9b4o$2b4o$b6o8b6o$2b4o$8o6b8o$2b4o$b6o5bobob4obobo$2b4o6b o3bo2bo3bo$8o2bob4ob2ob4obo$2b4o4b4obo4bob4o$b6o4b3o2b4o2b3o$2b4o7bo3b 2o3bo$2b4o6bo2b6o2bo$13bo2b4o2bo$3b2o10bob2obo$3b2o7bobob4obobo$2bo2bo $3b2o7b3ob4ob3o$2bo2bo4bobo10bobo$3b2o5b4ob6ob4o$2bo2bo6b3o6b3o$3b2o5b 4ob6ob4o$2bo2bo7bobo4bobo$3b2o6b2o10b2o$2bo2bo6b4o4b4o$3b2o6bo3bo4bo3b o$2bo2bo5bob10obo$11bob3ob2ob3obo$b6o3bob4ob2ob4obo$bob2obo3bobo10bobo $bob2obo5b2o3b2o3b2o$2b4o9bob2obo$13bob6obo$12bo3b4o3bo$11b3o3b2o3b3o$ 11b3o3b2o3b3o$11b4o6b4o$10b6ob2ob6o$11b4o2b2o2b4o$10b3o3b4o3b3o$14b2ob 2ob2o2$13b3o4b3o$14b3o2b3o$12b4o4b4o$12b4o4b4o$14bobo2bobo$10bobobobo 2bobobobo$12bo3bo2bo3bo$13b3o4b3o$14b3o2b3o$14b3o2b3o$12b5o2b5o$14b2o 4b2o$10b5obo2bob5o$14b2o4b2o$10b4o2b4o2b4o$12b4o4b4o$11b3o2b4o2b3o$11b obo8bobo$10bobo10bobo$12b3o6b3o$11b3o8b3o$12b3o6b3o$10b5o6b5o$11bobo8b obo$11bobobo4bobobo$11b3o8b3o$12b3o6b3o$11b3o8b3o$12b3o6b3o$10b3o10b3o $13b3o4b3o$11b3o8b3o$12b4o4b4o$10bobo10bobo$12bobo6bobo$11bo12bo$13b2o 6b2o$10b4o8b4o$12b2obo4bob2o$10bob2obo4bob2obo$13bo8bo36$2bo3bobo7bobo 5bobo8bobo5bobo7bobo3bo$b2obobobobobobobobobobobobobo4bobobobobobobobo bobobobobob2o$62o$62o$62o$62o$b2obobobobobobobobobobobobobo4bobobobobo bobobobobobobobob2o$2bo3bobo7bobo5bobo8bobo5bobo7bobo3bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ LOOP 305 ]]

(click above to open LifeViewer)

External links

• Diamoeba at Adam P. Goucher's Catagolue
• Gliders in diamoeba (discussion thread) at the ConwayLife.com forums
• MCell built-in Life rules: Diamoeba at Mirek Wójtowicz's Cellebration page