OCA:4diagonal: Difference between revisions
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===Oscillators=== | ===Oscillators=== | ||
Several new oscillators emerge. | 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.<ref | 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.<ref name="post149022" /> Many were found in the much more thoroughly-apgsearched rule {{cata|census/b34cs234c|B34c/S234c}}, and found to be compatible with 4diagonal. | ||
{{EmbedViewer | {{EmbedViewer | ||
|rle = x = 58, y = 120, rule = B34c/S23 | |rle = x = 58, y = 120, rule = B34c/S23 | ||
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|position = center | |position = center | ||
|viewerconfig = #C [[ WIDTH 1000 HEIGHT 675 ZOOM 6 ]] | |viewerconfig = #C [[ WIDTH 1000 HEIGHT 675 ZOOM 6 ]] | ||
|caption = Alien oscillator collection which don't work in life, marked by period. | |caption = 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. | ||
|style = width:300px; | |style = width:300px; | ||
}} | }} | ||
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 [[capped period-43 glider gun]] is rephased to period-41 in this rule. <ref name="post156100" /> | |||
===Stable circuitry=== | ===Stable circuitry=== | ||
Revision as of 22:58, 12 January 2026
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This page is under construction. Sorry for the inconvenience. |
| 4diagonal | |
| 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.[1] Many were found in the much more thoroughly-apgsearched rule B34c/S234c, and found to be compatible with 4diagonal.
| 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) |
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 capped period-43 glider gun is rephased to period-41 in this rule. [2]
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 | 1768P45H17V0 | 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.
References
External links
- B34c/S23 (4diagonal) & B34c/S234c (discussion thread) at the ConwayLife.com forums
- 4diagonal at Adam P. Goucher's Catagolue