OCA:Holstein

Holstein
x=0, y = 0, 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	Chaotic
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 and c/5.

x = 68, y = 69, rule = B35678/S4678 3b5o4b5o12b5o5b5o16b2o$2b3ob3o2b3ob3o13b4obob4o18b2o$4b2o3b2o3b2o11b4o b2obobob2ob4o12b6o$2b2ob3o4b3ob2o9bob2obobobobobob2obo11b8o$b3o5b2o5b 3o8bobo4b2ob2o4bobo11b8o$b4obo6bob4o10bo3bo5bo3bo12b2o6b2o$b2o4b2o2b2o 4b2o9bob3o7b3obo11b10o$4obo8bob4o11b3o5b3o$3bo4bo2bo4bo11bobo2b7o2bobo 9b14o$3bo2b2o4b2o2bo14b11o13b2o8b2o$6bo2b2o2bo14b3o5bo5b3o12bo6bo$2bob 2ob2o2b2ob2obo9b3obob3ob3obob3o$3bobo3b2o3bobo9b2obo3bo5bo3bob2o10b8o$ b2o3bo2b2o2bo3b2o9bo4bo5bo4bo14bo2bo$2obo3b6o3bob2o8bo4bo5bo4bo13b6o$ 2b2o3bob2obo3b2o12b2obo5bob2o16b4o$8b4o17bob2o2bobo2b2obo14b6o$6bobo2b obo16b2o2b5o2b2o15b6o$8b4o18bo3bobobo3bo15b2o2b2o$34bo3bo17b3ob2ob3o$ 32bobo3bobo$28bo3bobo3bobo3bo11bob6obo$29b6o3b6o$27b3ob2obo3bob2ob3o 13b4o$27bo3bo9bo3bo$29b5o5b5o$31b3o5b3o$31b5ob5o$31b3o5b3o$33b2o3b2o$ 30b4ob3ob4o$30b3o7b3o$32b4ob4o$34b2ob2o$34b5o$33b7o$35b3o$35b3o$35b3o 2$36bo$34bobobo$34b5o$32bobobobobo$34bobobo$34b5o$34b5o$33bob3obo$34b 5o$32bob5obo$32bob5obo$30b13o$30b13o$29b15o$29b15o$29b6obob6o$30b5obob 5o$30bobo7bobo$30bob3o3b3obo$30bobo7bobo$30bob3o3b3obo2$33b7o$32b2obob ob2o$34b2ob2o$32b3obob3o$34bobobo$32b3obob3o$34b2ob2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 WIDTH 700 HEIGHT 700 ]]

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

The 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 12 WIDTH 540 HEIGHT 700 ]]

(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]}

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