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.

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3bo16bo3bo121bobo191bo$224b3o18b3o95bo26b2o149b2o$107bo234bobo176bo$106b 3o232bo2bo173b2obo3b2o$105bobobo232b2o172bo2bob2o2b2o$105bobobo7b8o110b o280b2obo25bo$106b3o8bob4obo110b3o281bo5b2o18b3o$107bo9b8o113bo280b2o 5bo21bo$237b2o8b2o6b2o16bo250bo15b2o5b2o$246bo2bo4bo2bo15b3o248b2o13b 2o$240b2o3b6o2b6o17bo264bo9bo$239bobo4bo2bo4bo2bo17b2o274bobo$239bo7b 2o6b2o27bo2bob2obo2bo23bobobo2bobobo23b2o195b2o$91bo2bobobo18b2o120bo bo35b3o4b4ob2ob4o58b2o202b2ob2o$117b2o121b2o34bo2bo4bo2bob2obo2bo27bo 2bo3bo86bo140b2obo2bo$91bo2bo180bo140bobo144b2o$276bo2bo39bobobo2bobo bo84bo3bo130b2o$91bo2bobobo126b2o6b2o42b3o136bobo131b2o4bo2bo$113b2o2b 3o104bo2bo4bo2bo87bo2bo3bo67b2o17bo4b2o132b4o$91bo2bo3bo14b2o9b3o96b6o 2b6o116b3o42bo23bobo137bo$117bobo4b3o97bo2bo4bo2bo83bobobo2bobobo22bo 2bo39bobo25bo121bo11b5o$91bo2bobobo19bo5b3o98b2o6b2o8b2o151b2o26b2o119b obob2o7bo$127b3o113bo110b3o188bobobobo8bo$105b3o19b3o114b3o168bo126b2o bobobobo2bo4b2o$105b3o19b3o116bo31b2o135b2o125bo2bo2b2ob4o$105b3o168b 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Alien oscillator collection (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