Phoenix

From LifeWiki
Jump to navigation Jump to search
This article is about the general concept. For the 12-cell oscillator, see Phoenix 1.

A phoenix (plural phoenices or phoenixes) is a pattern all of whose cells die in every generation, but that never dies as a whole. A pattern that is a phoenix is also said to be phoenician.

The first discovered phoenix in Conway's Game of Life, phoenix 1, was a period-2 oscillator with 12 cells. A spaceship cannot be a phoenix in Life, and in fact every finite phoenix eventually evolves into an oscillator.[1]

An inherent property of phoenices is that its heat equals its population.

Every known finite phoenix oscillator has period 2. Infinite phoenix oscillators (agars) are known for periods 2, 4, 6, 8 and 12.[2] In January 2000, Stephen Silver showed that a period-3 oscillator cannot be a phoenix;[1] and in September 2019, Alex Greason showed that there are no period-5 phoenix oscillators.[3] The situation for other periods is unknown.

some avatars

As with any general pattern, there are innumerable instances of phoenices, some of which are striking enough to be shown on their own individual pages. Many are based on simple avatars such as the ones shown in the figure, which means that there would be considerable redundancy in exhibiting more than a few prototypes of any class of phoenices. The first pair (croaker and flutter respectively) were among the first discovered, along with the realization that they could be strung out quite arbitrarily into long filaments and even into closed loops.

Dominoes, either vertical or horizontal, can be stacked and even staggered slightly, as long as they are parallel and spaced by a single width. Unlike having monominoes and dominoes alternating, the chains are not flexible enough to create elaborate patterns.

On the other hand, monominoes alone can be used to create diagonal phoenix chains. Finite chains of this type quickly disintegrate, but in a departure from strict phoenicity the ends of the chains can sometimes be anchored. Such is the origin of the barberpole family.

The final example is a section of a phoenix agar incorporating avatars of the preceding styles. Note that while the blue lattice generates the red lattice, the red lattice does not regenerate the blue lattice; rather each generation is translated to the northeast by a single Life cell. The larger unit cells of the agar are 4×6, whose least common multiple (and hence the period of the agar as an oscillator) is 12.

Gallery

x = 200, y = 16, rule = B3/S23 4bo16bo19bo15bo19bo12bo17bo17bo12bo21bo7bo17bo7bo$2bobo16bobo17bobo13b obo17bobo8bobo15bobo15bobo12bobo19bobo5bobo15bobo5bobo$6bo12bo19bo5bo 9bo17bobo16bo11bo5bo11bo5bo6bobo5bo15bo5bobo17bo5bobo$2o22b2o19bobo12b 2o11bo6b2o4b2o14bobo15bobo12bo7bobo19bo6b2o17bo6b2o$6b2o10b2o18b2o14b 2o15bo20b2o16b2o6bo9b2o3bo24b2o24b2o$bo23bo22b2o11bo19bo5bo12b2o14bob o27b2o24bo25bo$3bobo14bo19bobo13bobo4bo6b2o22bo14bo15bobo4b2o26bo25bo $3bo22b2o14bo6bo8bo4bobo16b2o4b2o10bo13b2o9bo20bo23b2o24b2o$20b2o22bo 15bo11bo21b2o12b2o11bobo10bobo7bo15b2o24b2o$26bo23b2o14b2o14bo5bo9b2o 15bo5bo14bo5bobo25bo26bo$22bobo19b2o14b2o10b2o6bo12bo11bobo9bobo18bob o21bo22bo$24bo25bo15bo11bobo5b2o11bo5bo11bo22bo27b2o28b2o$46bobo13bob o9bobo15b2o7bobo58b2o20b2o6bo$48bo15bo11bo10bo13bo66bo21bobo5bo$89bob o72bobo19bobo5bobo$89bo76bo21bo7bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 WIDTH 1800 AUTOSTART GPS 2 LOOP 2 ]]
All p2 phoenices in a 16x16 box[4]
(click above to open LifeViewer)
RLE: here Plaintext: here

See also

References

  1. 1.0 1.1 Dave Greene (December 7, 2018). Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums
  2. Alex Greason (November 4, 2019). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  3. Alex Greason (September 29, 2019). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  4. wwei23 (November 17, 2021). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums

External links