C/3 diagonal: Difference between revisions
Added example spaceships for Day & Night and 3-4 Life |
Added example spaceships for Move and Sqrt replicator |
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'''c/3 diagonal''' is a diagonal [[speed]] that is equivalent to one third of the speed of light. | '''c/3 diagonal''' is a diagonal [[speed]] that is equivalent to one third of the speed of light. | ||
In [[Conway's Game of Life]] or any other rule without an B0, B1, B2, S4 or S5 transition, no [[spaceship]] can travel at this speed through a [[vacuum]].<ref name="njohnston" /> However, it is attainable in many other rules that do have an S4 or S5 transition, including [[Day & Night]], [[3-4 Life]], [[Move]], [[Star Trek]], [[Geology]], [[Dance]] and [[OCA:Castles|Castles]]. | In [[Conway's Game of Life]] or any other rule without an B0, B1, B2, S4 or S5 transition, no [[spaceship]] can travel at this speed through a [[vacuum]].<ref name="njohnston" /> However, it is attainable in many other rules that do have an S4 or S5 transition, including [[Day & Night]], [[3-4 Life]], [[Move]], [[Sqrt replicator rule|Sqrt replicator]], [[Star Trek]], [[Geology]], [[Dance]] and [[OCA:Castles|Castles]]. | ||
==Butterfly== | ==Butterfly== | ||
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|position = center | |position = center | ||
|caption = A synthesis of the c/3 diagonal spaceship | |caption = A synthesis of the c/3 diagonal spaceship | ||
|style = width:300px; | |||
}} | |||
==Move and Sqrt replicator== | |||
[[Move]] and [[Sqrt replicator rule|Sqrt replicator]] are two similar rules differing only by the presence of the B8 transition, and so have many patterns in common including these spaceships, which also both work in the two more rules with the S8 transition: | |||
{{EmbedViewer | |||
|rle = x = 32, y = 34, rule = B368/S245 | |||
13b2o$13b3o$11b2o2b2o$13b4o$10b2o4b2o$10bobo4bo$7bo2bobo2bobo$5bob2o6b | |||
obo$4bobobo2bo2b3o$8b3o3bo$6b3o$2bo2bobobo$bobob2o$bo2b2obo$3b2o$b3obo | |||
22b2o$b2obo18bo4b3o$4o18b3ob2o2b2o$2bo18bo2bo2bo2b2o$2bo19b2ob5o$o2bo | |||
12bo2bo3b5obo$3bo10b3obob2obo2b2o$b2o11b3ob4obo2bob2o$13b2o4bo4b4ob2o$ | |||
13b2o3bobo6bobo$19bo4b2o2bo$22bob2o$21bob2obo$22bob2o2$24b3o$24b2o$22b | |||
4o$22b2o! | |||
|viewerconfig = #C [[ TRACKLOOP 3 1/3 -1/3 THUMBSIZE 2 GPS 3 ZOOM 12 HEIGHT 600 AUTOSTART ]] | |||
|caption = Two spaceships that work in the 4 rules | |||
|position = center | |||
|style = width:300px; | |style = width:300px; | ||
}} | }} | ||
Revision as of 11:33, 4 July 2025
| c/3 diagonal | |
| Spaceship | No |
|---|---|
| Puffer | No |
| Rake | No |
| Wickstretcher | No |
| Gun | No |
c/3 diagonal is a diagonal speed that is equivalent to one third of the speed of light.
In Conway's Game of Life or any other rule without an B0, B1, B2, S4 or S5 transition, no spaceship can travel at this speed through a vacuum.[1] However, it is attainable in many other rules that do have an S4 or S5 transition, including Day & Night, 3-4 Life, Move, Sqrt replicator, Star Trek, Geology, Dance and Castles.
Butterfly
| The butterfly (click above to open LifeViewer) |
The butterfly is a c/3 diagnoal spaceship that works in the 128 outer-totalistic rules between B367/S346 and B3678/S0134678, including Day & Night for which it's proven the smallest.
3-4 Life
| 3-4 Life c/3d spaceship (click above to open LifeViewer) |
The above spaceship, despite its size, is quite rare in 3-4 Life, only commonly escaping from diagonally symmetric broths along the axis of symmetry. It works in the 64 rules between B34/S34 (aka 3-4 Life) and B3458/S034678.
Synthesis
In 3-4 life, this c/3 diagonal spaceship can be synthesized by 7 copies of the much more common c/3 orthogonal spaceship:
| A synthesis of the c/3 diagonal spaceship (click above to open LifeViewer) |
Move and Sqrt replicator
Move and Sqrt replicator are two similar rules differing only by the presence of the B8 transition, and so have many patterns in common including these spaceships, which also both work in the two more rules with the S8 transition:
| Two spaceships that work in the 4 rules (click above to open LifeViewer) |
References
- ↑ Nathaniel Johnston (October 30, 2009). "Spaceship Speed Limits in "B3" Life-Like Cellular Automata". Retrieved on December 12, 2016.