| Glimmering Garden
Glimmering Garden is an isotropic non-totalistic Life-like cellular automaton with Hensel notation B3-jknr4ity5ijk6i8/S23-a4city6c7c. It was devised by GUYTU6J on August 28, 2019.
Despite differing from the classic Game of Life by many non-totalistic transitions, Glimmering Garden have shown similar dynamics and engineering capabilities.
The period-240 oscillator cloverleaf is the most common oscillator and the second most common object arising from soups, due to the fact that an R-pentomino (or its 2-generation descendant B-heptomino) is a natural predecessor of it. It is a reflectorless rotating oscillator of loopability 1 and 3 (but not 2) with ⌘-shaped motion. It was this oscillator, found in other rules, that led to the discovery of Glimmering Garden.
The period-28 oscillator Julia is the third most common oscillator. The envelope resembles a Julia set, hence the name.
The period-44 oscillator butterfly is the fourth most common oscillator. There is a common non-trivial dimer of it as well. Without S4c this pattern becomes a replicator wave.
With the discovery of R-pentomino conduits (see below), oscillators of period 37 or above can be constructed. As of February 2021, the periods for which no oscillator is known are 10, 15, 20~22, 27, 29, 31~33, 35.
The glider from Life does not work in this rule. Naturally-occuring spaceships include the c/2 orthogonal T-ship, a c/4 orthogonal, a 3c/20 fireship-like orthogonal spaceship as well as several high-period c/2 ones, though some only in higher symmetrys.
Some non-exhaustive searches for c/2 and 2c/4 components have been carried out with Rust Life Search. Moreover, searching with ikpx2 has been done for c/4 diagonal and found 27 spaceships including tagalongs and extensible components as of February 2021; the smallest one is shown to the left.
FWKnightship constructed the first engineered spaceships from rake and puffers of simplified speed 4c/11, 8c/17 orthogonal and 7c/46 diagonal. Later, 16c/34 spaceships have also emerged from symmetric soups.
The bullet heptomino (Catagolue: here) is the smallest, fastest spaceship as well as the most common object arising from random soups. Its other phase is a t-tetromino plus one dot spark at the back, hence the name T-ship. Its significance for Glimmering Garden is to the same extent as the glider for Game of Life.
There are 29 distinct two T-ship collisions, 19 of which creates nothing, 6 creates a single T-ship (include 4 fly-by deletions and 2 kickbacks), one creates two T-ships and another one creates two blinkers. The remaining two is messy.
Infinite growth patterns
The most common linear growth pattern is a 32c/68 orthogonal double T-ship backrake, as shown on the right. It is the basis of many other linear growths, where the outputs are filtered by oscillators or crashed into other objects.
A large amount of natural T-ship guns are based on cloverleaf, Julia and butterfly. The smallest and fastest known gun is a true-period p13 T-ship gun on the left. With the discovery of stable T-ship duplicators, true-period T-ship guns with periods 51 or above can be constructed.
Other growth rates
A sqrtgun and caber tossers have been built. A T-ship to 24c/48o rake converter may be employed to build super-linear growth patterns. Sawtooth with a minimum repeating population of 188 has been found.
Giving off similar century-like sparks, the oscillators cloverleaf, Julia and butterfly are excellent for periodic technologies. For Julia, T-ship 90-degree reflector, 180-degree reflector, Heisenburp and AND gate have been found.
Stable technologies are of particular interest, most of which relies on tub, the smallest still life that functions as a versatile rock. The period-13 gun above is an example. The tub can also catalyse the evolution of R-pentomino/B-heptomino in various manners, which enables the construction of period-37 (or above) R-pentomino loop.
Besides the B-heptomino, T-ship is another vital signal carrier. After the discovery of a bait boat reaction with recovery time 51, Luka Okanishi constructed a stable T-ship duplicator giving 0-degree and 90-degree parity-preserved outputs. Parity-changing T-ship reflectors are also possible, completing a toolkit that is able to adjust the mod-4 timing of a T-ship by means of trombone slide.
Memory cells that require destructive read can be built from a snake, while permanent switch where information can be read non-destructively is realized with the still life xs8_5rk. Meanwhile, still-life factorys making tub, boat, beehive, etc are used in demultiplexer, regulator and pulse divider.
A barge can be a flintstone, in the sense that upon hitting certain patterns, two R-pentominoes emerge from it in a similar manner to the boat bait. This is useful in a c/4o-to-2T converter and a Hashlife-friendly period-64 double-barrelled gun.
- GUYTU6J (June 12, 2019). Re: Reflectorless Rotating Oscillators (RRO) (discussion thread) at the ConwayLife.com forums