User:Tropylium/Dense cloud
This draft page documents a terminological proposal for general use in Life or wider cellular automaton research.
Notes on a topic, probably to be split in multiple pages yet.
A cloud is any isolated region of activity in the evolution of a pattern; it may comprise any number of connected components.
As smaller patterns usually possess smaller lifespans, any smaller components of a cloud will, if they are let to evolve naturally, also usually stabilize before larger ones (in particular, they may be marginal sparks that have been output by the cloud). If a rule is nonexplosive, its clouds will tend towards ultimate stabilization as a finite set of objects — though e.g. puffer and gun engines exist as a marginal option. From this, the pigeonhole principle suggests a cloud will eventually leave only a single active connected component (though by this point it may have broken into multiple separate clouds).
In stabilizing CA, clouds have an observed tendency to evolve in roughly circular shapes.
A dense cloud is a cloud that is both compact and has dense interior, where all living cells in the interior die in the next step from overpopulation. Thus, only select boundary cells can survive, and some new cells may be born from them (and only them, in the absense of
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The boundary comprises all cells (live or dead) within the cloud or cluster that are in contact with its exterior.
- A bi-block and similar pseudo still lifes, mirrored cap and similar induction coil dimers, and the snake are simple examples of patterns with dead boundary cells.
The interior comprises all cells within the pattern that are not in contact with the exterior.
- In Life we have reason to extend the concept of the interior to cells with only one or two exterior neighbors.
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- A finger cell is a thin protrusion with seven exterior neighbors and one live neighbor; they are related to edge sparks, which may
- A vertex cell exists at the corner of the boundary. We can divide them further:
- Sharp vertices have six exterior neighbors, and in a compact cloud will have the environment S2a.
- Right vertices have five exterior neighbors, and in a compact cloud can have the environments S2c, S2e, S3i, S3a.
- Obtuse vertices have four exterior neighbors, and in a compact cloud can have the environments S2k, S3j, S3n, S4a.
- An edge cell has three exterior neighbors.
- Orthogonal edges can have the environments S2i, S3e, S3r, S4i, S4r, S5i.
- Diagonal edges can have the environments S2n, S3c, S3q, S4n, S4w, S5a.
- Other edge positions exist, such as vertex-like environments when adjacent to dead cells that are a part of the boundary rather than the exterior. Some of them are also "orthogonal" or "diagonal", but we reserve these terms for "solid" parts of the boundary.
In Life, the sharp and right vertices of a compact cloud always survive, obtuse ones often as well.
Example 1: The traffic light sequence
This common familiar four illustrates well dense cloud stages of evolution. Dying cells within an evolution step are indicated here by "x"; they can be seen to occur repeatedly in connected masses. New cell birth locations are not indicated for clarity.
....... ....... ....... ....... ....... ...o... ...o... ..oxo.. ..o.o.. ..ooo.. > ..xxx.. > ....... ....... ...o... ..ooo.. ....... ....... ....... ....... ....... .......
T-tetromino evolves into the bullet heptomino, a small dense cloud; its single interior, single edge and two obtuse corner cells all die, which results in two squiggles (a temporary blinker and a V spark).
....... ....... ....... ....... ...o... ...x... ....... ...o... ..x.x.. ...o... ..oxo.. ..o.o.. ....... > ..o.o.. > ..x.x.. > .o...o. ..xox.. ...o... ..oxo.. ..o.o.. ....... ...x... ....... ...o... ....... ....... ....... .......
These squiggles interact and in two generations give rise to a square octomino, another dense cloud. It results in a single diamond-shape squiggle, which is moreover a lively pattern.
....... ....... ....... ...o... ...o... ..ooo.. ..o.o.. ..xxx.. .o...o. .o...o. > .ox.xo. > .o...o. ..o.o.. ..xxx.. .o...o. ...o... ...o... ..ooo.. ....... ....... .......
This diamond grows inward into another dense cloud that yields then an octagonal squiggle / lively pattern.
......... ......... ......... ......... ....o.... ...ooo... ...ooo... ...xxx... ......... ..o...o.. ..x.x.x.. .o.....o. ..o...o.. > .oxx.xxo. > .o.....o. ..o...o.. ..x.x.x.. .o.....o. ...ooo... ...xxx... ......... ......... ....o.... ...ooo... ......... ......... .........
This grows into the last dense cloud step of the evolution (a mass of four X-pentominos), which finally resolves in four blinkers.
Example 2: B-heptomino to Herschel
The B-heptomino is not a squiggle, but has archetypal squiggle parents of six cells (as seen e.g. in Puffer 2) and seven cells (as seen at generation 11 of the R-pentomino). We begin here from the former. The B itself is only semi-dense, but its grandchild (a century–leg-tie) is denser; the intermediates are still rather squiggle-like:
....... ....... ....... ...o... ..ooo.. ....... ...o... ..ooo.. ..xxo.. .o..o.. ..ooo.. > ..oxx.. > ..o..o. > .ox..o. > .o...o. .x..o.. ..o.oo. ..x.oo. ...ooo. ..oooo. .....x. ....... ....... ....... ....o..
At this point we fast forward after chaotic development to generation 13, where the initial pre-pre-block has just now detached as its own cluster (not shown; it will still interact with the tail of the remaining pattern, but only to delay its stabilization). This slightly dust-like phase spawns now a proper dense cloud (if with most of its weight towards the bottom) plus obo spark. The squiggle produced by these leads to another dense cloud, which breaks into two squiggles.
....... ....... ...o... ...o... ..ooo.. ...o... ..oxo.. ..o.o.. .ox.xo. .o...o. ..oxo.. ..o.o.. .oo.oo. .xx.xx. ....... .o..o.. > .o..o.. > .o..o.. > oxx.x.. > o...... .oo.... .xxx... x...o.. ...ooo. .ooooo. ..o.... .xxx... ....x.. ....... ....o.. ....xo. ..x..x. ....... ....... ....... ..oxxx. ..x.... .x..o.. .....x. ...x...
Both of these evolve into their own dense clouds (the former simply the bullet heptomino) that break apart into squiggles (largely sparks); these follow space dust evolution for a moment to finally then result in the Herschel.
....... ....... ....... ...x... ....... ....... ...o... ..xox.. ...o... ..ooo.. ..ooo.. ..xxx.. ....... ..x.x.. ...o... .x...x. > ..oxo.. > ..x.x.. > ....... > .ooo... ....... ....... .o..... .xx.... ....... x...... .oxxx.. .x...x. ....... ....... .ooooo. .xxxxx. ....... .xx.... ....... ....o.. ..o.xo. .xx..x. ....... .......