C/3 diagonal

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 a B0, B1, B2, S4 or S5 transition, no spaceship can travel at this speed through a vacuum. 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

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

The butterfly (click above to open LifeViewer) Catagolue: here

The butterfly is a c/3 diagonal 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 [[ TRACK 1/3 -1/3 THUMBSIZE 2 GPS 3 ZOOM 50 HEIGHT 600 AUTOSTART ]]

3-4 Life c/3d spaceship (click above to open LifeViewer) Catagolue: here

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 outer-totalistic 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)

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 outer-totalistic rules with the S8 transition:

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! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ TRACK 1/3 -1/3 THUMBSIZE 2 GPS 3 ZOOM 12 HEIGHT 600 AUTOSTART ]]

Two spaceships that work in the 4 rules (click above to open LifeViewer)

Star Trek

Star Trek can support spaceships of many different speeds, including this c/3 diagonal found by LaundryPizza03 in 2020 and also works in the 3 other outer-totalistic rules between B3/S024 and B38/S0248:

x = 22, y = 22, rule = B3/S0248 14b3o$11b3obob2o$12b2o5bo$10bo4bo4bo$5b3obo4bo5bo$4b2ob4ob4o5bo$8bo3b 5obob2o$4b2obo2bo4b3o3bo$3bo3bobo5b2o2b2o$5obob2o5b2o2b2o$2o18bo$3b2o bo7bobobo$3bobo6b2o2b2o$o2b3o6bo2b2o$obo3bo6b2ob2o$ob3o2bo2bobo4bo$8b 2o4bob2o$6bobobobobobo$6bob3ob2o$6b2o4bo$11b2o$6b3o2b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART GPS 3 THUMBSIZE 3 ZOOM 32 WIDTH 840 HEIGHT 840 TRACK 1/3 -1/3 ]]

c/3d Star Trek spaceship (click above to open LifeViewer) Catagolue: here