C/3 diagonal: Difference between revisions

From LifeWiki
Jump to navigation Jump to search
More information. Maybe add information about reactions in Life which travel at this speed - e.g the burning of a crabstretcher's output used in the Speed Demonoid.
Added example spaceships for Day & Night and 3-4 Life
Line 9: Line 9:
'''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]], [[Star Trek]], [[Geology]], [[Dance]] and [[OCA:Castles|Castles]].
 
==Butterfly==
{{EmbedViewer
|rle          = x = 5, y = 5, rule = B3678/S34678
b3o$3obo$3b2o$3b2o$3bo!
|viewerconfig = #C [[ TRACKLOOP 3 1/3 -1/3 THUMBSIZE 2 GPS 3 ZOOM 50 HEIGHT 600 AUTOSTART ]]
|caption      = The butterfly
|position    = center
|style        = width:300px;
}}
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==
{{EmbedViewer
|rle          = x = 4, y = 4, rule = B34/S34
b3o$2b2o$o2bo$bo!
|viewerconfig = #C [[ TRACKLOOP 3 1/3 -1/3 THUMBSIZE 2 GPS 3 ZOOM 50 HEIGHT 600 AUTOSTART ]]
|caption      = 3-4 Life c/3d spaceship
|position    = center
|style        = width:300px;
}}
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:
{{EmbedViewer
|rle          = x = 80, y = 22, rule = B34/S34
7b2o$7b2o$6b4o2$55b4o$31bo19bo4b2o$2bo13bo13b2o18b2o$3o12b2o12b3o17b3o
$3o12b2o46bo$2bo13bo46b3o$63b3o$48bo14bo$48b2o26b3o$48b2o26b2o$48bo27b
o2bo$78bo4$52b4o$53b2o$53b2o!
|viewerconfig = #C [[ ZOOM 8 WIDTH 1000 ]]
|position    = center
|caption      = A synthesis of the c/3 diagonal spaceship
|style        = width:300px;
}}


==References==
==References==

Revision as of 09:59, 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, Star Trek, Geology, Dance and Castles.

Butterfly

x = 5, y = 5, rule = B3678/S34678 b3o$3obo$3b2o$3b2o$3bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ TRACKLOOP 3 1/3 -1/3 THUMBSIZE 2 GPS 3 ZOOM 50 HEIGHT 600 AUTOSTART ]]
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

x = 4, y = 4, rule = B34/S34 b3o$2b2o$o2bo$bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ TRACKLOOP 3 1/3 -1/3 THUMBSIZE 2 GPS 3 ZOOM 50 HEIGHT 600 AUTOSTART ]]
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:

x = 80, y = 22, rule = B34/S34 7b2o$7b2o$6b4o2$55b4o$31bo19bo4b2o$2bo13bo13b2o18b2o$3o12b2o12b3o17b3o $3o12b2o46bo$2bo13bo46b3o$63b3o$48bo14bo$48b2o26b3o$48b2o26b2o$48bo27b o2bo$78bo4$52b4o$53b2o$53b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 8 WIDTH 1000 ]]
A synthesis of the c/3 diagonal spaceship
(click above to open LifeViewer)

References

  1. ↑ Nathaniel Johnston (October 30, 2009). "Spaceship Speed Limits in "B3" Life-Like Cellular Automata". Retrieved on December 12, 2016.