User:Tropylium/B2aS13
- Names given here in bold are proposed, those in italics remain tentative.
B2a/S13, also Ant Nest, is an INT rule and one of the earlier-investigated nonexplosive B2 rules, proposed by myself (Tropylium) in 2012[1] and first flagged for further exploration by Extrementhusiast.[2]
The rule differs from various nearby rules with the growth type B2ce by the absense of a small c/2o spaceship / puffer / replicator engine, and is thus "flightless". It still has many lifeforms with the V-spark frontend. The V-spark by itself manages one cycle of movement, before interacting with its own back sparks to yield a domino and a blanker (see below).
Still lifes
The domino is ubiquitous, but a large variety of others exist. Common larger still lifes are the block (evolving from duoplet; and remaining a useful induction coil), and more specific to the rule, six-cell polyominoes plate and incline, the eight-cell polyplet nova, and the twelve-cell polyplet lozenge, which four can be also welded together from their exposed S1 ends to arbitrary sizes. Plate and its extensions have the useful property that, most of their immediately nearby dead cells already having three neighbors, no region of activity can come to damage the plate from this direction. They can be thus used, to an extent, to contain reactions or support oscillators (see below for the waterdrop on plate, ant on a plate, and the big fountain).
As the rule has only odd survival conditions, any still life, or connected component in a still life, must have an even number of cells.
A common large twelve-domino constellation Dodecanesia evolves from the 4-cell anchor shape of Seeds in 133 generations.
| "Dodecanesia" and its simplest ancestor (click above to open LifeViewer) |
All S3 environments can occur within a still life, though many are rare in natural still lifes. S3a remains the block. At six cells, plate shows S3i, S3e and S3r while incline shows S3j and S3r; clock and bunny-on-domino are the smallest still lifes with S3y (or also S1c), and attaching longer legs to the prepond stabilizes S3k. At eight cells, bunny-weld-plate or bunny-weld-incline are the smallest with S3q, arrowhead the smallest with S3n, and twin bunnies the smallest with S3c.
Oscillators
A large variety of oscillators occur already naturally. Common basic p2 oscillators are the ship flipper or skipper (evolving from diagonal line of three), the on-off crosshairs and the waterdrop on plate, of which the latter two can be supported also by larger stators.
The most common oscillator is the p4 variant of the blinker, which could be named blanker; from "bl4nker", as well as the fact that the two extra generations involve a step of no other changes that the center cell dying, i.e. "blanking". Two or three blankers can be welded at right angles to produce the bi-blanker and tri-blanker; these can attach to dominos or the exposed orthogonal ends found in most other still lifes.
Two blankers separated by (2, 3) create a p5, confused blankers, and extending both to tri-blankers creates a p7, confused tri-blankers.
Common unrelated p4s are hookspin and the sparky fountain, which can act as an eater or reflector.
The ants are a series of related large-period axially symmetric oscillators. The most basic is the p10 flipper worker ant and its p9 variant ant on a plate. Two placed face to face interact to become the p17 fighter ants.
Much more important is the p28 sparker shuttle queen ant, which can be used to construct guns and reflectors. A p13 dimer exists.
| p56 nova reigniter (click above to open LifeViewer) |
Spaceships
The only common basic spaceship is the three-cell c/4 diagonal miniglider, or in context simply, glider. It has in both of its frames the same appearence as the c/6 of rules like Just Friends, but lacking S2, avoids the tail-shaped phase. Minigliders with (0,4) or (4,0) offset will nontrivially interact with one another, which allows forming arbitrary polyomino clusters. Dot sparks will readily convert nearby dominos to minigliders from as many as four orientations (three away from the spark, one of them towards).
Several larger spaceships are known, including a rare but natural glide-reflective orthogonal 2c/4.
| The miniglider by itself, and a cluster of twelve in the shape of a dense phase of an LWSS (click above to open LifeViewer) |
Guns
The smallest known gun is a p84 by myself, based on a glider collision found by Extrementhusiast with a queen ant that produces a domino and a blanker: the former is released as the output by another queen ant, the latter is hassled by the first queen ant first into a domino and then into a glider heading back, which is then reflected back by two more queen ants. User Osiris constructed a flashier gun of the same period, noting a queen ant can also release a domino from a nova reignition, which can be then converted into a glider by yet another queen ant. Both can be extended to longer multiple-of-28 periods by moving back the glider-reflecting pair of queen ants or replacing it with a nova reflector.
| p84 guns (click above to open LifeViewer) |
References
- ↑ Tropylium (January 26th, 2012). SansDomino rulespace (discussion thread) at the ConwayLife.com forums
- ↑ Extrementhusiast (February 14th, 2012). Re: SansDomino rulespace (discussion thread) at the ConwayLife.com forums