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A '''period map''' of an oscillator displays different constituent cells of said oscillator differently, usually in different colors, as to highlight which constituent cells oscillate at certain periods. | A '''period map''' of an oscillator displays different constituent cells of said oscillator differently, usually in different colors, as to highlight which constituent cells oscillate at certain periods. | ||
Generally, | Generally, "period-1 cells" are marked with one of two possible colors: one color is used for [[stator]] cells which are permanently on, and another is used for cells which never turn on at all, i.e. "background" cells. This is an obviously useful distinction to make in rules such as [[Conway's Game of Life]], as the empty void around an oscillator is never worth analysing. However, in other cases such as a rule invariant under [[black-white reversal]] (e.g. [[Day and Night]]) being run on a [[bounded grid]], distinction between "always off" and "always on" cells is often less useful as they function identically to each other. | ||
The following table lists the cell colors which are used by the period maps [[LifeViewer]] produces: | |||
{| class="wikitable" | {| class="wikitable" | ||
! colspan="2" | Color | |||
! Usage | |||
|- | |||
| style="background-color:#000000" | | |||
| #000000 | |||
| Period-1 cells which are always off, i.e. are not "part" of the oscillator, but are still within its bounding box | |||
|- | |||
| style="background-color:#A8A8A8" | | |||
| #A8A8A8 | |||
| Period-1 cells which are always on, i.e. stator cells | |||
|- | |||
| style="background-color:#EEEEEE" | | |||
| #EEEEEE | |||
| Cells which oscillate at the full period, i.e. cells in a period-n oscillator that oscillate at period n | |||
|- | |||
| style="background-color:#808080" | | |||
| #808080 | |||
| Used to mark cells at the edge of a [[bounded grid]] | |||
|- | |||
| style="background-color:#606060" | | |||
| #606060 | |||
| Used to distinguish [[deathforcer]] cells from other cells that do not oscillate | |||
|- | |||
| colspan="2" | All other colors | |||
| Used for cells in an oscillator that do not oscillate at the full period, i.e. they oscillate at a subperiod | |||
|- | |||
| style="background-color:#505050" | | |||
| #505050 | |||
| This color is reserved for grid lines, as well as the outer borders of very large maps | |||
|} | |} | ||
=== Support === | === Support === | ||
The first well-known implementation of period maps was by [[Oscillizer]], which allowed for these to be displayed for valid sufficiently-low-period oscillators specifically in | The first well-known implementation of period maps was by [[Oscillizer]], which allowed for these to be displayed for valid sufficiently-low-period oscillators specifically in Conway's Game of Life. | ||
The [[Nakano]] utility, created in response to Oscillizer no longer working, is also capable of producing period maps. | The [[Nakano]] utility, created in response to Oscillizer no longer working, is also capable of producing period maps. | ||
As of December 2022, | As of December 2022, LifeViewer's ''Identify'' functionality also produces period maps for oscillators up to a period of 4194304, provided sufficient memory is available; as of April 2023, all supported 2-state rulespaces can have period maps created. | ||
Revision as of 17:07, 7 June 2023
Not to be confused with MAP strings, a common method of notating non-isotropic cellular automata.
A map is a visual diagram obtained from a pattern, generally an oscillator, which reveals and highlights specific properties of said pattern.
Period map
A period map of an oscillator displays different constituent cells of said oscillator differently, usually in different colors, as to highlight which constituent cells oscillate at certain periods.
Generally, "period-1 cells" are marked with one of two possible colors: one color is used for stator cells which are permanently on, and another is used for cells which never turn on at all, i.e. "background" cells. This is an obviously useful distinction to make in rules such as Conway's Game of Life, as the empty void around an oscillator is never worth analysing. However, in other cases such as a rule invariant under black-white reversal (e.g. Day and Night) being run on a bounded grid, distinction between "always off" and "always on" cells is often less useful as they function identically to each other.
The following table lists the cell colors which are used by the period maps LifeViewer produces:
| Color | Usage | |
|---|---|---|
| #000000 | Period-1 cells which are always off, i.e. are not "part" of the oscillator, but are still within its bounding box | |
| #A8A8A8 | Period-1 cells which are always on, i.e. stator cells | |
| #EEEEEE | Cells which oscillate at the full period, i.e. cells in a period-n oscillator that oscillate at period n | |
| #808080 | Used to mark cells at the edge of a bounded grid | |
| #606060 | Used to distinguish deathforcer cells from other cells that do not oscillate | |
| All other colors | Used for cells in an oscillator that do not oscillate at the full period, i.e. they oscillate at a subperiod | |
| #505050 | This color is reserved for grid lines, as well as the outer borders of very large maps | |
Support
The first well-known implementation of period maps was by Oscillizer, which allowed for these to be displayed for valid sufficiently-low-period oscillators specifically in Conway's Game of Life.
The Nakano utility, created in response to Oscillizer no longer working, is also capable of producing period maps.
As of December 2022, LifeViewer's Identify functionality also produces period maps for oscillators up to a period of 4194304, provided sufficient memory is available; as of April 2023, all supported 2-state rulespaces can have period maps created.