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

Still lifes

With transition S3-a, a block dies instantly. Other than that the rule exhibits larger varieties of still lifes compared with the classic Game of Life.

Oscillators

There are three characteristic common oscillators, of period 240, 28 and 44 respectively. They are all very sparky and thus play an important role in technologies.

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 also a reflectorless rotating oscillator with ⌘-shaped motion, albeit of loopability 1. 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.

With the discovery of R-pentomino conduits (see below), oscillators of period 37 or above can be constructed. At the time of writing, the periods for which no oscillator is known are 10, 11, 15, 16, 19~25, 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 c/4 diagonal spaceship
(click above to open LifeViewer)

Naturally-occuring spaceships include the c/2 orthogonal T-ship, a c/4 orthogonal and a 3c/20 fireship-like orthogonal spaceship, though the latter only in higher symmetrys. Moreover, some non-exhaustive searches for c/2 and 2c/4 components have been carried out with Rust Life Search.

Searching with ikpx2 has been done for c/4 diagonal and found a 250-cell spaceship, as shown to the left, along with a tagalong.

FWKnightship constructed the first engineered spaceships from rake and puffers of simplified speed 4c/11, 8c/17 orthogonal and 7c/46 diagonal.

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 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), 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.

Linear growth patterns

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 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, T-ship guns with periods 51 or above can be constructed.

Signal Circuits

Oscillating

Giving off similar century-like sparks, the oscillators cloverleaf, Julia and butterfly are excellent for signal circuits. 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 T 0 PAUSE 2 T 133 PAUSE 2 ]]
Stable T-ship duplicator
(click above to open LifeViewer)

Stable technologies are also of 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. A parity-changing T-ship reflector is 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.

Memory cells that require destructive read (such as demultiplexer) can be built from tub or boat factorys, while permanent switch where information can be read non-destructively is realized with the still life xs8_5rk.

References

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

External links