User:GUYTU6J/OCA:Glimmering Garden

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Glimmering Garden
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

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 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, 19~27, 29, 31~33, 35.

Spaceships

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 a c/2 orthogonal spaceship. It 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.
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, one creates two blinkers. The remaining two is messy.

Apart from said T-ship, a c/4 orthogonal and a 3c/20 orthogonal spaceship have occured in soups as well, though the latter only in higher symmetrys.

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

Linear growths

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 output of this backrake are filtered by oscillators or crashed into other objects.

The third most common one is a 14c/92 diagonal puffer (Catagoluehere) whose output is solely Julias.

Various T-ship guns are based on cloverleaf, Julia and butterfly. The smallest and fastest known gun is a true-period p13 T-ship gun, as shown on the left.

Signal Circuits

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)

Tub, the smallest still life, can act as a good rock. The period-13 gun above is an example. The tub can also catalyse the evolution of R-pentomino/B-heptomino, which enables the construction of period-37 (or above) R-pentomino loop.

Giving off similar century-like sparks, the oscillators cloverleaf, Julia and butterfly are also excellent for signal circuits. For Julia, T-ship 90° reflector, 180° reflector, Heisenburp, demultiplexer and AND gate have been found.

References

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

External links