User:GUYTU6J/OCA:Glimmering Garden

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Glimmering Garden
x = 0, y = 0, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c ! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ RANDOMIZE THUMBLAUNCH OFF THUMBNAIL THUMBSIZE 2 ]]
An example soup in B3-jknr4ity5ijk6i8/S23-a4city6c7c (click above to open LifeViewer)
Rulestring 23-a4city6c7c/3-jknr4ity5ijk6i8
B3-jknr4ity5ijk6i8/S23-a4city6c7c
Character Chaotic


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.

Patterns

Despite differing from the classic Game of Life by many non-totalistic transitions, Glimmering Garden have shown similar dynamics and engineering capabilities.

Still lifes

Without transition S3a, a block dies instantly, while the existence of B4i6i prohibits longer induction coils. Other than those the rule exhibits larger varieties of still lives compared with Life.

Oscillators

There are three common, sparky volatile oscillators, of period 240, 28 and 44 respectively, that characterize Glimmering Garden as the minimum isotropic non-totalistic rule to support the trio.

x = 6, y = 5, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c bob2o$6o$b2o$2b3o$3bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 20 AUTOSTART ZOOM 8 X 9 Y -5 ]]
Cloverleaf, a period-240 oscillator
(Catagoluehere)
(click above to open LifeViewer)
x = 9, y = 9, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 5bo$4b2ob2o$5bo2bo$2o5b2o$2o$2bo$bo$bobo$b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 20 AUTOSTART ZOOM 16 X -3 Y 1 ]]
Julia, a period-28 oscillator
(Catagoluehere)
(click above to open LifeViewer)
x = 18, y = 18, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c b2o$obo$o$2o$2bo$6bo$5b3o$5bo$4bo$3b3o$11bo$11b2o$8bob2o$8b2o$8bo$13bo2b2o$ 14bo2bo$14b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 20 AUTOSTART ZOOM 10 X -1 ]]
Butterfly, a period-44 oscillator
(Catagoluehere)
(click above to open LifeViewer)

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[1], 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.

Spaceships

x = 68, y = 61, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 20bobo$19bob3o$22bobo$24b2o$21bob2o$21b2o$21bo$b3o$o2bo$2o2bo$23b3o$ 24bo$24bobo2$23bobo2$17b3o5bo$17bo$17bo2bo$18b3o3$39bobo$38bob3o$41bob o$43b2o$40bob2o$40b2o$40bo4$42b3o$43bo$43bobo2$13b3o26bobo$12bo2bo$12b 2o22b3o5bo$36bo$36bo2bo$37b3o21bobo$60bob3o$63bobo$65b2o$62bob2o$62b2o $62bo3$44bo$41bobob3o16b3o$41b2obo2bo17bo$44bo2bo17bobo$44b3o$35b3o26b obo$34bo2bo$34b2o22b3o5bo$58bo$58bo2bo$59b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART GPS 20 TRACK 7/46 -7/46 ZOOM 4 WIDTH 500 HEIGHT 500 LOOP 92 ]]
A 3-engine 14c/92d spaceship
(click above to open LifeViewer)
x = 56, y = 53, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c bo11b3o$4o9bo$o2bo10bob3o$bobo7b3obo3bo$b4o5b2ob2o4bo$b4ob3o2bo2bo2b2o bo$7bo2bo3bo4b2o$5b2o4bob3o2b3o$8b3o8b2o$9bo7bobobo$11b2o3bo3b2o$13b2o $12bo10bo$12b3o4b4obo$14b2o3bo4bo$15bob2o5bo$17b2o4bobo$18b2o2bobobo$ 22bo3bo$17b2ob4o2bo$17bobo2bo$17b2o7bo$17b2o5b2obo$17b2o5bo$20bo13bo$ 19bobo10b3o$20bobo4bobob2o$21bobo2b2ob2o2b2o2b4o$22bobo2b2o4bo2bob2o2b o$23b2o4bo7b2obobo$30bob2o5bobobo$31bobo6bobo$32bobo8bo$33bobo8b2o$34b obo3b2o$35bob4obob2o$36bobobobobobo$37bo2bo2bo2bo$41bob2ob2o$42bob2o2b o$45bo2b2o$42bo5bobo$42b3o2bobo$44bo2bo2bo$45bob2obobo$46bo3b3o$51bo$ 52bo$51b3o$48b3o$48bo$54b2o$50b4o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART GPS 2 TRACK -0.25 -0.25 ZOOM 4 LOOP 4 ]]
A 250-cell c/4 diagonal spaceship
(Catagoluehere) (click above to open LifeViewer)

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.

T-ship

x = 174, y = 152, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c o4bo3bobo3bobobo2bo3bo3bo3bo4bo4bobo$80bobobobo3bo2bo6bo3bo49bobobo$ob o2bo2bo3bo4bo4bo3bo3bo3bobo2bo2bo$80bo2bo2bo3bo3bobo3bo55bo$o2bobo2bo 3bo4bo4bobobo3bo3bo2bobo2bo2bobo$80bo5bo3bo6bo2bo3bo51bo$o4bo2bo3bo4bo 4bo3bo3bo3bo4bo2bo4bo$80bo5bo3bo3bobo4bobo52bo$o4bo3bobo5bo4bo3bo3bo3b o4bo4bobo$156bo10$9bo4bo144bo5b2o$6bob2o4b2obo138bob2o4b3o$9bo4bo26bo 50bo66bo5b2o2$41bo50bo$40b3o48b3o4$14bo$9bo4b2obo21bo49bo$6bob2o4bo21b ob2o46bob2o$9bo29bo49bo$163b3o$163b3o$164bo3$14bo$14b2obo$9bo4bo144bo$ 6bob2o146bob2o$9bo34bo114bo2$44bo$43b3o2$14bo$14b2obo$14bo$9bo29bo101b obobobobobobobobobobobobobobobobo$6bob2o26bob2o$9bo29bo49bo$149bobobo 3bobobo2bo$89bo$88b3o58bo4bo2bo6bo$14bo144bobo$14b2obo131bo4bo2bo6bo$ 14bo$149bobobo3bobobo2bobobo$9bo79bo$6bob2o76bob2o$9bo35bo43bo68bo2$ 45bo112bo$44b3o110b3o4$15bo$9bo5b2obo20bo119bo$6bob2o5bo20bob2o116bob 2o$9bo29bo119bo6$15bo$15b2obo$9bo5bo$6bob2o$9bo150bo$38b3o$38b3o119bo$ 39bo119b3o2$15bo$15b2obo$15bo$9bo29bo119bo$6bob2o26bob2o116bob2o$9bo 29bo119bo7$15b2o$9bo4b3o$6bob2o5b2o$9bo153bo$41b3o$41b3o119bo$42bo119b 3o3$15b2o$14b3o$9bo5b2o22bo119bo$6bob2o26bob2o116bob2o$9bo29bo119bo$ 90b3o$90b3o$91bo2$15b2o$14b3o$15b2o$9bo79bo$6bob2o76bob2o$9bo79bo$42b 3o114b3o$42b3o114b3o$43bo116bo$15b2o$14b3o$15b2o2$9bo29bo119bo$6bob2o 26bob2o116bob2o$9bo29bo119bo11$44b3o$44b3o$45bo5$39bo49bo5bo$36bob2o 46bob2o5b2obo$39bo49bo5bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 1.8 ]]
All 29 distinct two T-ship collisions
(click above to open LifeViewer)

The bullet heptomino (Catagoluehere) 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.

Some 3T syntheses has been discovered for boat, ship, long boat and blinker. In-depth investigation is yet to be done.



Infinite growth patterns

Linear growth

The rule has abundant rakes, puffers and guns.

x = 11, y = 8, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 5bo$4bobo$4b3o3$bo7bo$obo5bobo$bo7bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART GPS 20 ZOOM 16 Y -4 THUMBSIZE 3 ]]
The period-13 T-ship gun
(Catagoluehere)
(click above to open LifeViewer)
x = 27, y = 26, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 10bo5bo$9b2o5b2o$8b2o7b2o3$13bo$12b3o$12bobo$12bobo$4bo2bo4bobo4bo2bo$ 5b2o6bo6b2o$2o23b2o$o25bo$3obo17bob3o$4b2o15b2o$3b2o17b2o7$9bo2bobo2bo $8b3o5b3o$9bo3bo3bo$10bob3obo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART GPS 20 TRACK 0 -8/17 ZOOM 7 Y 7 LOOP 68 ]]
The backrake(Catagoluehere)
(click above to open LifeViewer)

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.

The third most common one is a 14c/92 diagonal puffer (Catagoluehere) arising from a double interaction between a cloverleaf and a Julia, making the outputs solely Julias.

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.

Side products from c/4 diagonal ikpx2 search include several wickstretchers, puffers, and growing spaceships consisting of a fuse burning at c/7d, 2c/10d, 4c/26d and 13c/61d.

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.

Signal Circuits

Oscillating

x = 21, y = 12, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 3bo$ob2o$3bo$13b3o$13bobo2$12b3o$13bo$19b2o$17bo2bo$15b2ob3o$15b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 8 THUMBSIZE 4 WIDTH 500 HEIGHT 300 AUTOSTART GPS 14 LOOP 57 PAUSE 2 T 56 PAUSE 2 ]]
Period-28 Heisenburp reaction
(click above to open LifeViewer)

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

Also see: Appendix 1: Miscellaneous construction practice
x = 73, y = 73, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 37bo$36bobo$37bo$32b3o$26bo7bo$25bobo2b2ob2o$26bo5bo$29bo2bo$30b2obo2b 2o$29bobo2b2ob2o12bo$30bo6bo3b2o7bobo$30b2o2b3o4bo9bo$18bo16bo$17bobo 5bo$18bo5b3o$23bo2bo10bo$22b3o2bo8bobo8b2o$23bo2b3o8bo10bo10bo$32bo13b 3o9bobo$31bobo25bo$10bo21bo$9bobo$10bo45bo$45bo9b3o$16b3o25bobo9bobo$ 16bobo26bo12b2o7bo$18bo5bo30bob2o7bobo$23bobo29b2o10bo$24bo30bo$63bobo $10bo50b2obo2bo$10b2o41bo7bob2o2bo$52bobo10b2o2bo$53bo10bo2bobo$bo7bo 6bo44bobo3b3o$obo5b3o4bobo42b2obo$bo6bo2bo4bo39bo4bo2bo6bo$9bob2o42bob o4b3o5bobo$3b3o3bobo44bo6bo7bo$3bobo2bo10bo$3bo2b2o10bobo$5bo2b2obo7bo 41b2o$5bo2bob2o50bo$7bobo$17bo30bo$5bo10b2o29bobo$4bobo7b2obo30bo5bo$ 5bo7b2o12bo26bobo$14bobo9bobo25b3o$15b3o9bo$16bo45bo$61bobo$40bo21bo$ 13bo25bobo$12bobo9b3o13bo$13bo10bo10bo8b3o2bo$24b2o8bobo8bo2b3o$35bo 10bo2bo$46b3o5bo$47bo5bobo$37bo16bo$21bo9bo4b3o2b2o$20bobo7b2o3bo6bo$ 21bo12b2ob2o2bobo$35b2o2bob2o$40bo2bo$40bo5bo$38b2ob2o2bobo$38bo7bo$ 38b3o$35bo$34bobo$35bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART GPS 20 ZOOM 4 ]]
Period-37 R-pentomino loop
(click above to open LifeViewer)
x = 64, y = 35, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 37bo$36bobo$37bo6$31bobo$32bo2$32bo2$31bo$30bobo$31bo8$2o25bo$3o21bob 2o$2o25bo34bo$61bobo$34b2o26bo$34bobo$35bo$55bo$49bo2bobo$41bo6bobo4bo $40bobo6bo$41bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART GPS 20 ZOOM 9 THUMBSIZE 3 HEIGHT 480 WIDTH 600 X 20 Y 0 LOOP 134 PAUSE 2 T 133 PAUSE 2 ]]
Stable T-ship duplicator
(click above to open LifeViewer)

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.

Further elaboration have resulted in exact-timing (synchronized) Boolean logic AND, OR, XOR, ANDNOT gates, and eventually, a stable Rule 110 unit cell proving the rule Turing-complete.

x = 69, y = 37, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 65bo2$65bo$64b3o7$27bo39bo2$27bo39bo$26b3o37b3o16$3bo14bo24bo14bo$ob2o 11bob2o21bob2o11bob2o$3bo14bo24bo14bo3$23b2obo37bobo$23bob2o35b2ob2o$ 62bobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART GPS 20 ZOOM 8 LOOP 64 PAUSE 2 T 42 PAUSE 2 T 52 PAUSE 2 T 63 PAUSE 2 ]]
Memory bits (click above to open LifeViewer)

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.

Occasionally, a boat and an xs8_2dic can serve as an eater.

References

  1. GUYTU6J (June 12, 2019). Re: Reflectorless Rotating Oscillators (RRO) (discussion thread) at the ConwayLife.com forums

External links