Mod

The mod of an oscillator or spaceship is the smallest number of generations that it takes for it to reappear in its original form, possibly subject to some rotation or reflection.

Oscillators

On a square grid

The mod of a given oscillator may be equal to its period, but it may also be a quarter of the period (for oscillators that rotate 90 degrees every quarter period) or half the period (for other oscillators that rotate 180 degrees every half period, oscillators with 180 degree rotational symmetry that rotate 90 degrees every half period, and also for flippers).

b2o$o$3bo$b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART THUMBSIZE 2 ZOOM 12 GPS 2 LOOP 2 ]] The toad is an example of an oscillator with a mod identical to its period, as its two phases are completely distinct and one cannot be mapped to the other purely through rotation and translation (click above to open LifeViewer) RLE: here Plaintext: here

2bo$obo$bobo$bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART THUMBSIZE 2 ZOOM 12 GPS 2 LOOP 2 ]] The clock is an example of an oscillator with a mod which is half its period, as both of its phases can clearly be turned into each other by a diagonal reflection (click above to open LifeViewer) RLE: here Plaintext: here

3bo$3bobo$bo$6b2o$2o$6bo$2bobo$4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART THUMBSIZE 2 ZOOM 12 GPS 2 LOOP 2 ]] The phoenix 1 is another example of an oscillator with a mod which is half its period, as both of its phases are interchangeable through orthogonal mirroring (click above to open LifeViewer) RLE: here Plaintext: here

x = 21, y = 21, rule = B3/S23 9bo$8bobo2$6bo3b2o$5bo5bo$6bobo$8b2o6bo$16bo$2bo5b2o4b3o$2bo11b2o$3o7b 2o2b2o2b3o$2o6bob2o4b3o$2o2b3obobo5b3o$2b3o$2b3o6bo$10bobo2$8bo3b2o$7b o5bo$8bobo$10b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART THUMBSIZE 2 ZOOM 12 GPS 2 LOOP 4 ]] Sixty-nine is an example of an oscillator with a mod which is a quarter its period, as all four of its phases are identical and differ only by 90-degree rotation (click above to open LifeViewer) RLE: here Plaintext: here

On a hexagonal or triangular grid

The mod of an oscillator can be identical to its period, but it can also be half of its period (for oscillators which flip halfway through their evolution), a third of its period (for oscillators that rotate 120 degrees a third of the way through their evolution), or a sixth of its period (for oscillators that rotate 60 degrees a third of the way through their evolution).

Oscillators with a mod one sixth of their period must be centered around either a hexagonal cell or a triangular grid's vertex.

Other definitions

As the Conway's Game of Life community is a mathematical community, the term "mod" is sometimes used for its standard mathematical definition, such as "≡ 2 (mod 8)" for numbers that are 2 greater than a multiple of 8. This definition is not to be confused with the mod of a pattern.

See also

• Kinetic symmetry
• Reflectorless rotating oscillator

External links

• Mod at the Life Lexicon