Difference between revisions of "Mod"
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The mod of a pattern may be equal to its [[period]], but it may also be a quarter of the period (for oscillators that [[:Category:Non-flipping oscillators that turn 90 degrees|rotate 90 degrees]] every quarter period) or half the period (for other oscillators that [[:Category:Non-flipping oscillators that turn 180 degrees|rotate 180 degrees]] every half period, oscillators with 180 degree rotational symmetry that rotate 90 degrees every half period, and also for [[flipper]]s). | The mod of a pattern may be equal to its [[period]], but it may also be a quarter of the period (for oscillators that [[:Category:Non-flipping oscillators that turn 90 degrees|rotate 90 degrees]] every quarter period) or half the period (for other oscillators that [[:Category:Non-flipping oscillators that turn 180 degrees|rotate 180 degrees]] every half period, oscillators with 180 degree rotational symmetry that rotate 90 degrees every half period, and also for [[flipper]]s). | ||
{{EmbedViewer | {| | ||
|{{EmbedViewer | |||
|position = left | |position = left | ||
|pname = toad | |pname = toad | ||
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|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. | ||
}} | }} | ||
{{EmbedViewer | |{{EmbedViewer | ||
|position = center | |position = center | ||
|pname = | |pname = clock | ||
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 ZOOM 64 WIDTH 600 HEIGHT 600 GPS 2 LOOP 2 ]] | |viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 ZOOM 64 WIDTH 600 HEIGHT 600 GPS 2 LOOP 2 ]] | ||
|caption=The [[ | |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. | ||
}} | }} | ||
|{{EmbedViewer | |||
|position = right | |||
|pname = phoenix1 | |||
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 ZOOM 64 WIDTH 600 HEIGHT 600 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. | |||
}} | |||
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{| | |||
|{{EmbedViewer | |||
|position = center | |||
|pname = sixtynine | |||
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 ZOOM 16 WIDTH 600 HEIGHT 600 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. | |||
}} | |||
|} | |||
==External links== | ==External links== | ||
{{LinkLexicon|lex_m.htm#mod}} | {{LinkLexicon|lex_m.htm#mod}} |
Revision as of 17:47, 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).
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External links
- Mod at the Life Lexicon