OCA:4diagonal

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 the 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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156bo4bo103bo29b3o126b2o4bo$78bo2bo3bo14b2o9b3o148bo6bo63b2o37bo4b2o158b obo$104bobo4b3o147bo8bo55b2o5bo2bo8b2o25bo4b3o22b2o2bo131b2o$78bo2bob obo19bo5b3o147bo8bo55b2o5bo2bo8bobo31bo22bo$114b3o144bo8bo63bobo9b2o23b o8b2o19b5obo$92b3o19b3o145bo6bo100b2o8bob4o6bo9bobobo$92b3o19b3o146bo 4bo72b2o9bobo15b2o5bobo3bobo5b2o$92b3o170b2o74bobo8bo2bo5b2o7bo6b4obo 8b2o$95b3o5bo238b2o8bo2bo5b2o18b2o8bo$95b3o4bobo249b2o27bo$95b3o9b2o274b 3o4bo11bobobo$102b3o2b2o275b2o4bo10b5obo$390bo11bo$345b3o54b2o2bo2$103b 2o240bo2bo53b3o$103b2o241b3o29b2o22b2o$377bobo22bo$377bo$376b2o33b2o$ 411bo$409bobo$346b2o56bo4b2o$346b2o55bobo$402bo3bo$403bobo$404bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 1600 HEIGHT 800 ZOOM 2 ]]

Alien oscillator collection which don't work in Life, marked by period. Right oscillators also work in B34c/S234c, the few left oscillators don't work in Life or B34c/S234c. (click above to open LifeViewer) RLE: here Plaintext: here

x = 56, y = 62, rule = B34c/S23 24bo$22b4o$12b2o7b2o3bo6b2o$7bo4b2o6bo3b2o7b2o$7b3o11b4o$10bo11bo$9b2o $31b2o$32bo$32bobo$33bobo$2o32bo3b2o$2obo34b2o$4bo$bo$2bob2o$4b2o5$40b 3o$39bo$42bo$38bo$39b2o$42b3o$41b2obo$42b2o4$43b2o$30b2o10bobo$30b2o 13bo$40b2o3bo$39bo5bo$36b2o6bo$37bo4b2o6$40bo$39b3o8b2o$38b2o2bo7b2obo $39b4o11bo$37bobo11bo$16b2o18bo2bo12bob2o$16b2o3bo14bo2bo14b2o$20bobo 14b2o$21bobo$23bo$23b2o$45b2o$26b2o17bo$22bo7bo7b2ob2o3b3o$21bo7b2o3b 4o5bo4bo$21bo5b4o3b2o7bo$22b2ob2o7bo7bo$37b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 600 HEIGHT 700 ZOOM 6 ]]

A p288 herschel hassler (click above to open LifeViewer) Catagolue: here

x = 44, y = 44, rule = B34c/S23 34bo$32b3o$31bo$26b2o4bo$26b3ob2obo$26b2obobobo$32bo$29b3o$28b3o$2o26b 3o$bo2b2o22b3o$bobo2bo22bo$2bo2b2o$5bobo2bo$5b3ob2o$10bo15b2o$3b2ob2o 18b2o$3b2o23bo$26b2o$26b2o6$39bo$38bobo$34bo$32bo3b2o2bo$32bo4b3o$32b o6b2o$14bo19bobob2obo$14bo22bo2bobo$13b3o22b2o2bo$42b2o2$14b2o$11b2ob 3o$10bobo$10bo4b4o$11bo$12bo$9b3o$9bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 600 HEIGHT 700 ZOOM 7 ]]

A p124 pi-heptomino hassler (click above to open LifeViewer) Catagolue: here

Despite being less explored compared to near-life rules like B34c/S234c, B38/S23, and B3/S238, the rule was proven omniperiodic before all of those rules and life because the period-43 glider gun is rephased to period-41 in this rule.

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	1768P35H17V0	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.

External links

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