Difference between revisions of "Mod"

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Line 8: Line 8:
|position    = left
|position    = left
|pname        = toad
|pname        = toad
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 ZOOM 64 WIDTH 600 HEIGHT 600 GPS 2 LOOP 2 ]]
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 ZOOM 32 WIDTH 480 HEIGHT 480 GPS 2 LOOP 2 ]]
|caption=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.
|caption=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.
}}
}}
Line 14: Line 14:
|position    = center
|position    = center
|pname        = clock
|pname        = clock
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 ZOOM 64 WIDTH 600 HEIGHT 600 GPS 2 LOOP 2 ]]
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 ZOOM 32 WIDTH 480 HEIGHT 480 GPS 2 LOOP 2 ]]
|caption=The [[clock]] is an example of an oscillator with a mod which is half its period, as both of its phases are a three-cell-long line and one can clearly be turned into the other by a 90-degree rotation.
|caption=The [[clock]] is an example of an oscillator with a mod which is half its period, as both of its phases are a three-cell-long line and one can clearly be turned into the other by a 90-degree rotation.
}}
}}
Line 20: Line 20:
|position    = right
|position    = right
|pname        = phoenix1
|pname        = phoenix1
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 ZOOM 64 WIDTH 600 HEIGHT 600 GPS 2 LOOP 2 ]]
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 ZOOM 32 WIDTH 480 HEIGHT 480 GPS 2 LOOP 2 ]]
|caption=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.
|caption=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.
}}
}}
Line 28: Line 28:
|position    = center
|position    = center
|pname        = sixtynine
|pname        = sixtynine
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 600 GPS 2 LOOP 4 ]]
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 ZOOM 8 WIDTH 480 HEIGHT 480 GPS 2 LOOP 4 ]]
|caption=[[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.
|caption=[[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.
}}
}}

Revision as of 17:49, 20 April 2021

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

The mod of a pattern 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 32 WIDTH 480 HEIGHT 480 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 32 WIDTH 480 HEIGHT 480 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 are a three-cell-long line and one can clearly be turned into the other by a 90-degree rotation.
(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 32 WIDTH 480 HEIGHT 480 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 8 WIDTH 480 HEIGHT 480 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

External links

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