OCA:4diagonal

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4diagonal
x=64, y = 64, rule = B34c/S23 ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE2 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	23/34c B34c/S23
Character	Chaotic

4diagonal is an Isotropic non-totalistic rule that differs from regular Life by one isotropic birth transition B4c. Any true or pseudo still-life from life with four live corners (& only 4 live corner cells) situated around a cell will either become an oscillator (e.g. a 2x2 grid of blocks) or will fail (e.g. the standard eater 2). This rule was proven omniperiodic 1 week before Conway's Game of Life.

Patterns

Oscillators

Several new oscillators emerge. Interestingly, most traffic light predecessors from Life query B4c without any permanent evolutionary changes. Periods containing oscillators not in common with Life include 2, 3, 11, 12, 32, 38 and 90. Many were found in the much more thoroughly-apgsearched rule B34c/S234c, and found to be compatible with 4diagonal.

x = 38, y = 102, rule = B34c/S23 4bo$3bobo$b3ob3o$o7bo$b3ob3o$3bobo$4bo3$2ob2o$o3bo2$o3bo$2ob2o3$4bo$2b3o$2o3bo$bo3bo$bo3b2o$2b3o$2bo4$2bobobo$2b5o$2bobobo2$3bobo$b2o3b2o$4bo$b2o3b2o5$12b3o$b2o7b2o2bo7b2o$b2o7bo2b2o7b2o$10b3o6$16b2o$16b2o5$15b3o$15bobo$15bo2bo$16bobo$16b3o4$7b3o$b2o4bo2b2o8b2o$b2o4b2o2bo8bobo$9b3o9b2o2$16b2o9b3o$16bobo8bo2b2o4b2o$17b2o8b2o2bo4b2o$29b3o4$20b3o$20bobo$20bo2bo$21bobo$21b3o5$21b2o$21b2o7$10b2ob2o$9b2o3b2o$10b2ob2o$11b3o$2b3o7bo3$11bo7b3o$10b3o$9b2ob2o$8b2o3b2o$9b2ob2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 1475 HEIGHT 675 ZOOM 4 ]]

Alien oscillator collection which don't work in life, marked by period. Left oscillators also work in B34c/S234c, the few right oscillators don't work in life or B34c/S234c. (click above to open LifeViewer)

Stable circuitry

The Snark and Snark64, along with several Herschel Conduits, are preserved in this rule. Notably, the Colour-preserving semi-Snark becomes a RT49 reflector on its own in this rule.

Spaceships

Despite the single-transition change from life, there are several new speeds of ships, including a large 17c/35 orthogonal ship, two minuscule c/17 orthogonal ships, and

Below is a table of the smallest ships:

Direction	Speed	Period	Smallest known	Minimum # of cells
orthogonal	c/2	2	66P2H1V0	66
		4	lightweight spaceship	9
	c/3	3	25P3H1V0.1	25
	c/4	4	37P4H1V0	37
	c/5	5	Spider	58
		10	68P10H2V0	68
	c/6	6	56P6H1V0	56
	c/7	7	16P7H1V0	16
	c/10	10	Copperhead	28
	c/17	17	30P17H1V0	28
	2c/5	5	51P5H2V0.1	51
	2c/7	7	Weekender	36
	17c/35	45	FIX LINK	1768
diagonal	c/4	4	glider	5
	c/5	5	58P5H1V1	58
	c/6	6	77P6H1V1	77
	c/8	8	walrus	68

Infinite Growth

Besides the 17c/35 puffer, the century is a dirty glide-symmetric 12c/55 (42c/220 unsimplified) puffer in this rule. There is also a period-46 glider gun with only one twin bee. Notably, The period-43 glider gun is rephased to p41, which proved the rule omniperiodic.

External links

• B34c/S23 (4diagonal) & B34c/S234c (discussion thread) at the ConwayLife.com forums
• 4diagonal at Adam P. Goucher's Catagolue