OCA:Holstein

Holstein
x=64, y = 64, rule = B35678/S4678 ! #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
Rulestring	4678/35678 B35678/S4678
Rule integer	238056
Character	Stable
Black/white reversal	B35678/S4678
Strobing dual	B0124/S01235
Checkerboard dual	B12cn3-e4cny5-c6ei7/S02-ei3c4-ejr5e6-cn8

Holstein is a Life-like cellular automaton with rulestring B35678/S4678.

This rule treats black cells on white backgrounds the same as white cells on black backgrounds, and is therefore self-complementary. Black regions are surrounded by froth and tend to eventually collapse starting from the corners, but can be stabilized in various ways by oscillators on their boundaries.

x = 27, y = 20, rule = B35678/S4678 2bo2bobobobobobobobobo$2bobobobobobobobobobobobo$bob21ob2o$2b23o$b25o$ ob23obo$b25o$ob23obo$b25o$ob23obo$b25o$ob23obo$b25o$ob23obo$b25o$b25o$ 25o$2b23o$bo2b2obobobobobobobob3obo$6bobobobobobobobo2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ZOOM 15 WIDTH 500 HEIGHT 500 GPS 2 AUTOSTART ]]

A period 2 way to stabilize a black region (click above to open LifeViewer)

There are no still lifes, since the lack of S3 implies that on a still life's boundary, there must exist pairs of adjacent on-cells, one with four contiguous adjacent off-cells (outside of the pattern's minimal convex hull), and, due to their minimum of three other neighbours each, between them must trigger B3a or B3i in at least one of these.

Seminatural oscillators are known of all even periods up to 36, and odd periods 3, 5, 7, 9, 15, 17, 21 and 27.

There are known spaceships of orthogonal speeds c/3, c/4, c/5, and c/7.

x = 133, y = 69, rule = B35678/S4678 3b5o4b5o8b5o5b5o5b5o3b2ob2o3b5o5b5ob5o8b4o10b9o10b4o$2b3ob3o2b3ob3o9b4obob4o6bob2obob9obob2obo6b2obob2o8b8o7b4o3b4o8b6o$4b2o3b2o3b2o7b4ob2obobob2ob4o3b3obob9obob3o4b13o5b8o7b11o8b6o$2b2ob3o4b3ob2o5bob2obobobobobob2obo4b2obobobobobobobob2o7b9o8bo4bo8b4o3b4o6b3o4b3o$b3o5b2o5b3o4bobo4b2ob2o4bobo5b3obob5obob3o5b3o3b3o3b3o3b10o5bob4ob4obo3b4obo2bob4o$b4obo6bob4o6bo3bo5bo3bo6b6obobobob6o8b3ob3o8bo6bo6bobo7bobo5b3o4b3o$b2o4b2o2b2o4b2o5bob3o7b3obo5bob3o4bo4b3obo5b3o3bo3b3o4b10o5b2ob2o3b2ob2o4b12o$4obo8bob4o7b3o5b3o8bob3o3b3o3b3obo21b2o8b2o22b4o2b4o$3bo4bo2bo4bo7bobo2b7o2bobo7b5ob3ob5o13bo8b2obob4obob2o3b3o7b3o3bob2obo2bob2obo$3bo2b2o4b2o2bo10b11o8b7ob3ob7o7b3o3b3o6bo8bo7b3o3b3o8bobo2bobo$6bo2b2o2bo10b3o5bo5b3o5b7ob3ob7o9b5o9bob4obo7b3obobob3o4b2ob2o4b2ob2o$2bob2ob2o2b2ob2obo5b3obob3ob3obob3o4bob3ob7ob3obo7bo3bo3bo23b4ob4o7b2o6b2o$3bobo3b2o3bobo5b2obo3bo5bo3bob2o5bobob7obobo9b9o7b8o6b13o3b5o4b5o$b2o3bo2b2o2bo3b2o5bo4bo5bo4bo5bobob2ob5ob2obobo9bo3bo12b2o11b9o5b3obo4bob3o$2obo3b6o3bob2o4bo4bo5bo4bo6b5obobobob5o9bob3obo9b6o8b11o4bobo8bobo$2b2o3bob2obo3b2o8b2obo5bob2o8bo5bobobo5bo10bobobo10b6o9b9o7bobo4bobo$8b4o13bob2o2bobo2b2obo8bo2bo7bo2bo12b3o10bob4obo8bob5obo5b2obo6bob2o$6bobo2bobo12b2o2b5o2b2o9b2o3bo3bo3b2o10b7o8bob4obo10b2ob2o8b3obo2bob3o$8b4o14bo3bobobo3bo7bobob2o7b2obobo10b3o26bo2bobo2bo4b16o$30bo3bo11bobo13bobo10b3o9b2ob4ob2o20b5o6b5o$28bobo3bobo9bobobo9bobobo38bobo5bobo4b3ob6ob3o$24bo3bobo3bobo3bo5bobobo9bobobo24b6o22b2ob2o6b2ob2o$25b6o3b6o6bobobobo5bobobobo37b4o5b4o8b4o$23b3ob2obo3bob2ob3o6bobo9bobo28b2o26bobo6bobo$23bo3bo9bo3bo5bob2o9b2obo39b4obob4o7b8o$25b5o5b5o8b3o9b3o41b3obob3o6bo3b4o3bo$27b3o5b3o9b5o7b5o38b13o4b5o2b5o$27b5ob5o9b3obo7bob3o40b9o9bob2obo$27b3o5b3o9b3o11b3o38b13o5b10o$29b2o3b2o11b2obo9bob2o40b9o9bo4bo$26b4ob3ob4o9bobo9bobo41b9o8b8o$26b3o7b3o7bob2o11b2obo41b5o12bo2bo$28b4ob4o10b2o13b2o43b3o10b10o$30b2ob2o89b2o$30b5o86bobo2bobo$29b7o$31b3o86b2o2b2o2b2o$31b3o85b3obo2bob3o$31b3o86b10o$118bob10obo$32bo85bob10obo$30bobobo84b12o$30b5o85b10o$28bobobobobo84b8o$30bobobo85bobob2obobo$30b5o$30b5o86b8o$29bob3obo$30b5o85b10o$28bob5obo85b2o2b2o$28bob5obo83b2ob4ob2o$26b13o84bo2bo$26b13o$25b15o$25b15o$25b6obob6o$26b5obob5o$26bobo7bobo$26bob3o3b3obo$26bobo7bobo$26bob3o3b3obo2$29b7o$28b2obobob2o$30b2ob2o$28b3obob3o$30bobobo$28b3obob3o$30b2ob2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 WIDTH 1120 HEIGHT 595 ]]

Spaceships of speeds c/3, c/4, c/5 and c/7 (click above to open LifeViewer)

The width-21 odd-symmetric c/4 orthogonal spaceship has a smaller asymmetrical stabilisation.

x = 21, y = 34, rule = B35678/S4678 3b5o5b5o$5b4obob4o$b4ob2obobob2ob4o$bob2obobobobobob2obo$bobo4b2ob2o4b obo$3bo3bo5bo3bo$2bob3o7b3obo$5b3o5b3o$2bobo2b7o2bobo$5b11o$2b3o5bo5b 3o$b3obob3ob3obob3o$2obo3bo5bo3bob2o$2bo4bo5bo4bo$2bo4bo5bo4bo$4b2obo 5bob2o$3bob2o2bobo2b2obo$4b2o2b5o2b2o$4bo3bobobo3bo$8bo3bo$6bobo3bobo $6bobo3bobo$7b2o3bo$6b3obo$6b5o$6bo$5b4o$5bo2b2o$5b4obo$4b6o$5b4o$4bo b4o$4bobobo$6bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ZOOM 16 WIDTH 540 HEIGHT 700 AUTOSTART GPS 4 TRACK 0 -1/4 ]]

(click above to open LifeViewer) Catagolue: here

c/4 diagonal and c/2 orthogonal spaceships are impossible, c/3 is the orthogonal speed limit and c/5 is the diagonal speed limit.^{[citation needed]}

Linear growth

The even-width c/5 frontend can also serve as the frontend of a wickstretcher.

x = 14, y = 44, rule = B35678/S4678 6b2o$6b2o$4b6o$3b8o$3b8o$2b2o6b2o$2b10o2$14o$b2o8b2o$3bo6bo2$3b8o$5bo2bo$4b6o$5b4o$4b6o$6b2o$5b3obo$4bob2obo$7b2o$5b5o$6bo$6b5o$7bo$7bobo$6bo2$7b2o2$5bobo$5bobo$5b2obo$6bo$5b2ob2o$8bo$4b6o$6b2obo$5b5o$5b4obo$4bob4o$5b6o$4bob3o$6bo2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ZOOM 12 WIDTH 540 HEIGHT 700 ]]

(click above to open LifeViewer) Catagolue: here

External links

• Holstein (B35678/S4678) (discussion thread) at the ConwayLife.com forums
• Holstein at Adam P. Goucher's Catagolue
• Holstein at David Eppstein's Glider Database
• Holstein (B35678/S4678) at David Eppstein's page in the Fano Experimental Web Server (archived copy)
• Paul Rendell's Holstein Cellular Automata Page