User:GUYTU6J/OCA:Glimmering Garden

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Glimmering Garden
熠熠种花
x=0, y = 0, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE THUMBLAUNCH OFF THUMBNAIL THUMBSIZE 2 GRID ZOOM 4 WIDTH 500 HEIGHT 500 LABEL 90 -20 2 "#G" AUTOSTART PAUSE 2 GPS 8 LOOP 256 ]]
LifeViewer-generated soup (refreshes with page)
Rulestring 23-a4city6c7c/3-jknr4ity5ijk6i8
B3-jknr4ity5ijk6i8/S23-a4city6c7c
Character Chaotic

Glimmering Garden (Chinese name: 熠熠种花) is an isotropic non-totalistic Life-like cellular automaton devised by GUYTU6J on August 28, 2019.

Rule definition

Birth (left) and survival (right) ransitions used by Glimmering Garden. Code: white=background, gray=gridline, black=ON neighbouring cell, lime=OFF neighbouring cell, yellow=OFF center cell, blue=ON center cell.

Same as the classic Game of Life, Glimmering Garden is a 2-state rule on a square grid with range-1 Moore neighbourhood (i.e. Life-like). A cell will be ON in the next generation if its neighbourhood matches any of the (non-totalistic) configurations above up to reflection and/or rotation (isotropic). In Hensel notation this is expressed as B3-jknr4ity5ijk6i8/S23-a4city6c7c, which is used by Golly and LifeViewer.

Patterns

Despite differing by many non-totalistic transitions, Glimmering Garden have shown similar dynamics and engineering capabilities to Life.

Still lifes

Without transition S3a, a block dies instantly, while the existence of B4i6i prohibits longer induction coils and B5k renders loaf unstable. Other than those the rule exhibits larger varieties of still lives compared with Life; the smallest asymmetric still life, for instance, is the 6-cell bobo$ob2o$bo! (xs6_2da, domino at tub) which does not persist in Life.

The most common still lives are:

Name / rle Apgcode Major predecessors Approximate relative frequency

out of all objects (out of 1.00)

Tub xs4_252 3o$bo$3bo! 0.08374
Cis-boat at boat xs10_25bkc 3o$bo$3bo! 0.05178
Long ship xs8_35ac bo$3o$2bo$2bo$3bo! giving two copies of 2b2o$bobo$o2bo$3o! 0.04397
Boat xs5_253 - (Modified from tub, long ship, etc) 0.04382
Ship xs6_356 bo$3o$o2bo$bobo! 0.01895
bo$ob2o$bobo$b2o! xs8_2da6 3o$bo$3bo! (Interrupted halfway) 0.00856
domino at tub xs6_2da - 0.00706

The listed tub and cis-boat at boat predecessor arises highly frequently; in 134 generations it develops a D4_x4-symmetric constellation consisting of two copies of each said still life aligned diagonally.

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 10 AUTOSTART ZOOM 8 X 9 Y -5 ]]
Cloverleaf, a period-240 oscillator
(click above to open LifeViewer)
Catagoluehere
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 10 AUTOSTART ZOOM 16 X -3 Y 1 ]]
Julia, a period-28 oscillator
(click above to open LifeViewer)
Catagoluehere
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 10 AUTOSTART ZOOM 10 X -1 ]]
Butterfly, a period-44 oscillator
(click above to open LifeViewer)
Catagoluehere

The period-240 oscillator cloverleaf is the most common oscillator as well as object[note 1] arising from soups. Several natural evolutionary sequences such as 3o$bo$3bo! (before annihilating) and bo$3o$o2bo$bobo! mentioned above give rise to copies of its predecessor, namely, R-pentomino or its 2-generation descendant B-heptomino (possibly with some spark cells tied to both). 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. An octomino predecessor for it, 2bo$b3o$2obo$bo!, can be seen above at generation 41 of cloverleaf.

The period-44 oscillator butterfly is the fourth most common oscillator. It arises from a heptomino bo$3o$2b2o$2bo! or the namesake butterfly sequence o$2o$obo$b3o! in Life. There is a common non-trivial dimer of it with a 7-cell predecessor b3o$obo$2o! as well. Without S4c in the rule, this pattern becomes a replicator wave.

The rule has been known to be omniperiodic since July 2021, although for p21 there is only a least-common-multiple oscillator.

#C I am an OCA RLE created for the following article: #C https://conwaylife.com/wiki/User:GUYTU6J/OCA:Glimmering_Garden #C As a big oscillator stamp collection, I need an independent page #C for the ease of updating that page. x = 1567, y = 1867, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 7bo13bo5b2o5bo5b2o12b2o4b2o4bo5b2o7b2o5b2o6b2o3b2o38bo2bo2bo7bo30bo5bo 108bo5bo7bo24bob2o27bo29b2o78bo2bo2bo7bo2bo2bo22bo4bobo37bo13b2o4b2o 70bo2bo2bo7bo25bo61bo67bo7bo2bo2bo7bo69bo77bo2bo2bo13bo7bo5bo18b2o5bo 12bo96bo2bo2bo7bo2bo2bo7bo31bo129bo2bo2bo7bo2bo2bo7bo2bo2bo$6bobo11bob o3bobo4bobo3bo2bo2b2obo3bo2bo3bobo3bob2o3bobobo3bo2bo5bobo4bo5bo37bob 2ob2obo5bobo28bobo3bobo106bobo3bobo5bobo23b2obo26bobo28bo3bo2bo7bo14bo 48bob2ob2obo5bob2ob2obo20bobo2bob2o36bobo12bo3b2obo69bob2ob2obo5bobo 23bobo51bob2o4bobo65bobo5bob2ob2obo5bobo67bobo75bob2ob2obo11bobo5bobo 3bobo16bobo4bobo5bobo2bobo4bo89bob2ob2obo5bob2ob2obo5bobo29bobo32bo94b ob2ob2obo5bob2ob2obo5bob2ob2obo$7bo13bo5bo4bobo5b2o3bob2o3b2o5b2o5bobo 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683bo14bo40b3o429bo169bobo$682b3o12bobo197bo272bobo165bo3bo$698bo187bo 9b3o9bo59bo202bo163bob2o2b2o$885bobo8b3o8bobo57bobo368bo3bobo$680bobob obo58bo140bo21bo59bo372bob2o$481bo2bo2bo7bo2bo2bo32b2o6bo68bo68bobobob o58bobo144bo9bo439bo$480bob2ob2obo5bob2ob2obo32bo5bobo66bobo132b3o145b 2o5b2o273bo$481bo2bo2bo7bo2bo2bo32bo7bo28bo39bo277b3ob3o3b3ob3o268bobo 164bo$481bo5bo7bo5bo32b2o34bobo109b3o208b2o5b2o59bo213bo164bobo$480bob o3bobo5bobo3bobo68bo5bo105bo208bo9bo57bobo116bo261bo$481bo5bo7bo5bo18b 2o54bobo170bo33bo102bo21bo52bo116bobo244bo$481bo2bo2bo7bo5bo18bobo54bo 170bobo31bobo100bobo19bobo169bo244bobo5bo$480bob2ob2obo5bobo3bobo19bo 21bo40bo163bo33bo102bo9bo11bo414bob2o4bobo$481bo2bo2bo7bo5bo20b2o19bob o38b3o308bobo426bo7bo$487bo7bo5bo38bo3bo39bob2o308bo$486bobo5bobo3bobo 34bob2o2b2o$487bo7bo5bo38bo3bobo739bobobo19bo6bo$481bo2bo2bo7bo2bo2bo 20b2o19bob2o738bob3obo17bobo3b2obo$480bob2ob2obo5bob2ob2obo19bo21bo 741bo3bo19bo4bobo$481bo2bo2bo7bo2bo2bo18bobo763b2o$520b2o57bo$578bobo$ 534b2o25b3o15bo$534bo7bo18bobo21bo$535bo5bobo17bo2b2o18bobo$534b2o6bo 22bo19bo75bo7bo2bo2bo7bo2bo2bo23b2o45bo2bo8b2o$563b3o2bo91bobo5bob2ob 2obo5bob2ob2obo23bo44bob2obo4bobo2bo$561b2o4bobo91bo7bo2bo2bo7bo2bo2bo 23bobo22bo21bo2bo4bob2o2bo$560b2obo4bo92bo13bo7bo5bo24bo22bobo29bo2bob 2o$561b2obo9bo85bobo11bobo5bobo3bobo23bo23bo34bo$563b3o7bobo21bo63bo 13bo7bo5bo22b2obo$564b3o7bo21b3o62bo7bo2bo2bo7bo2bo2bo22bobo$565b2o28b o2bo61bobo5bob2ob2obo5bob2ob2obo22bo38bo31bo$565bo33bo61bo7bo2bo2bo7bo 2bo2bo61bobo29bobo$598b3o60bo7bo19bo62bo27bo3bo$594bo65bobo5bobo17bobo 47bo13b2o23bob2o2b2o46bo2bo2bo13bo7bo2bo2bo99bo35bo2bo2bo7bo5bo7bo5bo 38bo96bo2bo2bo7bo2bo2bo7bo2bo2bo38bo$583b2obo3bo2bo67bo7bo19bo23bo23bo bo10bobo27bo3bobo43bob2ob2obo11bobo5bob2ob2obo97bobo33bob2ob2obo5bobo 3bobo5bobo3bobo36bobo94bob2ob2obo5bob2ob2obo5bob2ob2obo36bobo$584b3o3b 2o6bo12bob2o46bo7bo2bo2bo7bo2bo2bo48bo11b2obo29bob2o44bo2bo2bo13bo7bo 2bo2bo99bo35bo2bo2bo7bo5bo7bo5bo38bo96bo2bo2bo7bo2bo2bo7bo2bo2bo38bo$ 585bo11bobo11b2obo45bobo5bob2ob2obo5bob2ob2obo22bo38bo31bo52bo13bo7bo 5bo141bo7bo5bo7bo5bo141bo7bo5bo7bo5bo$598bo62bo7bo2bo2bo7bo2bo2bo22b3o 121bobo11bobo5bobo3bobo139bobo5bobo3bobo5bobo3bobo40bo2bo95bobo5bobo3b obo5bobo3bobo$576bo260bo13bo7bo5bo66bo34bo39bo7bo5bo7bo5bo40bob3o96bo 7bo5bo7bo5bo15bo$575bobo195bo57bo2bo2bo13bo7bo5bo65bobo32bobo32bo2bo2b o7bo2bo2bo7bo2bo2bo38b2obo3bo95bo7bo5bo7bo5bo14bobo$576bo5bo128bobobo 3bobo50bob2o54bob2ob2obo11bobo5bobo3bobo65bo30bo3bo32bob2ob2obo5bob2ob 2obo5bob2ob2obo37bobo3bobo93bobo5bobo3bobo5bobo3bobo14bo$581bobo126bob 3obobob2o38bo2bo7bo2bo56bo2bo2bo13bo7bo5bo66b2o26bob2o2b2o33bo2bo2bo7b o2bo2bo7bo2bo2bo38b3o4bobo93bo7bo5bo7bo5bo$582bo128bo3bo3bo39bob2obo4b obo2bo56bo19bo7bo5bo64bobo30bo3bobo37bo13bo13bo46bo94bo7bo5bo7bo5bo25b o$529bo184b2o3b2o39bo2bo5b2ob2o56bobo17bobo5bobo3bobo48bo14b2obo32bob 2o36bobo11bobo11bobo139bobo5bobo3bobo5bobo3bobo23bobo16bo$528bobo240bo 59bo19bo7bo5bo48bobo15bo34bo39bo13bo13bo141bo7bo5bo7bo5bo25bo16bobo$ 529bo6bo294bo2bo2bo13bo7bo2bo2bo49bo85bo2bo2bo13bo13bo141bo7bo2bo2bo7b o2bo2bo43bo$535bobo292bob2ob2obo11bobo5bob2ob2obo21b3o109bob2ob2obo11b obo11bobo21bo117bobo5bob2ob2obo5bob2ob2obo18bo7bo$536bo294bo2bo2bo13bo 7bo2bo2bo21bo2bo74bo35bo2bo2bo13bo13bo21bobo37bo79bo7bo2bo2bo7bo2bo2bo 18b3o$886bo77bobo89bobo37bobo125bo2bo25bo$886bo4bo73bo88b2obo38bobo 128b2o4bo18b3o$881bo4b3o2bo163bo39b2o2bo123bo2b2o23b2obo$554bo325bobo 172bo44bo120b2obo27bo$546bo2bo3bobo325bo172bobo43bo120bobo29bo$546bo3b o3bo500bobo41bobo120b2o$546bo3bo401bo98bo4bo43bo155b3o$547bo2bo400bobo 96bobo185bo$547b3o402bo98bo185bobo$1110bo127bo$552bo392bo144bo18bobo 145bo$551bobo390bobo142bobo18bo145bobo$552bo392bo144bobo164bo$523bo 567bo$522bobo566bo$523bo137bo7bo2bo2bo7bo2bo2bo34bo2bo361bob2o$660bobo 5bob2ob2obo5bob2ob2obo32bob2obo359bobo$526b3o132bo7bo2bo2bo7bo2bo2bo 34bo2bo359bobobo$525bo2bo132bo13bo7bo5bo398bobo$525bo3bo130bobo11bobo 5bobo3bobo398bo$521bo3bo3bo131bo13bo7bo5bo22bo22bo$520bobo3bo2bo131bo 7bo2bo2bo7bo5bo21bobo20bobo$521bo138bobo5bob2ob2obo5bobo3bobo21bo18bo 3bo328bo$661bo7bo2bo2bo7bo5bo22b2o14bob2o2b2o327bobo$661bo13bo7bo5bo 20bobo18bo3bobo326bobo3bo28bo$660bobo11bobo5bobo3bobo19b2obo20bob2o 327bo3bobo26bobo$539bo121bo13bo7bo5bo22bo22bo330b3obo28bo$538bobo120bo 7bo2bo2bo7bo2bo2bo376bo2bo$539bo6bo113bobo5bob2ob2obo5bob2ob2obo$545bo bo113bo7bo2bo2bo7bo2bo2bo34bo2bo344bo$546bo176bob2obo342bobo$724bo2bo 344bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 1600 HEIGHT 1900 ZOOM 1 ]]
Stamp collection for 16 still lives and 747 oscillators (period<1000) as of June 10, 2022 (click above to open LifeViewer)
RLE: here Plaintext: here

The periods for which statorless oscillator exists are 4, 12 (also strictly volatile), 14, 24+12n (p12 T-ship reflector), 28 (see above, also strictly volatile), 30, 44 (see above), 56+28n (p28 reflector), 60+30n (p30 reflector), 80 (see above, also strictly volatile), 88+44n (p44 gun-based reflector, not shown), 240 (see above, also strictly volatile). [note 2]

Spaceships

The glider from Life does not work in this rule. Spaceships from official apgsearch symmetries are listed below:

Category Speed Apgcode Info
c/2 orthogonal (1,0)c/2 xq2_1b1 T-ship, the second most common object from C1. Some trivial flotillae are not separated by apgsearch. See section below for details
(2,0)c/4 xq4_0gn20uz133 Two T-ships with period-4 block tagalong, first found from Rust Life Search
(12,0)c/24 xq12_6e6x7oghewehgo7x6e6 and xq12_y2gom3as88sa3mogz1b1yg1b1 Two T-ships escorting two B-heptominoes, from even bilateral symmetries
(24,0)c/48 xq48_37... and xq48_y3...
(36,0)c/72 xq72_y2...
(48,0)c/96 xq96_yz... Two B-heptomino pair puffers
(24,0)c/48 xq48_277zw27d6y5be4zw277 Two T-ships escorting a 4-tick descendant of 3o$bo$3bo!, making a would-be p12 cloverleaf puffer from C1
8c/17 orthogonal (16,0)c/34 xq34_y08... and xq34_y0g... Two engines that alone would be a 32c/68 backrake, from bilateral symmetries; the latter one with even symmetry is the smallest known
(32,0)c/68 xq68_yk... and xq68_yu... Engines are the same as above but with larger spatial distance, from C2 symmetries
(64,0)c/136 xq136_y1... Engines are the same as above, from even bilateral symmetries
c/4 orthogonal (1,0)c/4 xq4_nmkz31 The second smallest and fastest spaceship with distinctive speed, being non-monotonic as well, which has a 5T synthesis that is intrinsically a T+blinker+two dots reaction
3c/20 orthogonal (3,0)c/20 xq20_dadz373 Quite similar to the fireship in Life: symmetric, non-monotonic, with wide and sparky rear end
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 10 TRACK 7/46 -7/46 ZOOM 4 WIDTH 480 HEIGHT 480 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
(click above to open LifeViewer)
Catagoluehere

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. Of these, the 4c/11 (unsimplified 24c/66) spaceships are the largest; even the minimal 2-engine form has 167×56 or at least 457 cells.


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 ]] #C [[GPS 8]]
All 29 distinct two T-ship collisions
(click above to open LifeViewer)

The bullet heptomino is the smallest and fastest spaceship. 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 90-degree kickback and one 180-degree kickback; both kickback involve 3o$obo$bo!), one creates two T-ships via a teardrop-like sequence and another one creates two parallel blinkers. The remaining two is messy.

Some 3T syntheses has been discovered for tub, boat, ship, long boat and blinker. In-depth investigation including 3T, 4T, etc collision enumeration and component collection is yet to be done.

FWKnightship has demonstrated that a blinker may serve as a construction elbow by finding a set of PUSH, PULL and FIRE (sideways) elbow operations with 4~6 synchronized T-ships each. The minimum separation is 51 ticks, suitable for simple signal circuitry built with tubs and boats (see below).

Infinite growth patterns

Linear growth

The rule is inhabited by 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 10 ZOOM 20 Y -2 THUMBSIZE 4 ]]
The period-13 T-ship gun
(click above to open LifeViewer)
Catagoluehere
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 10 TRACK 0 -8/17 ZOOM 7 Y 7 LOOP 68 ]]
The 32c/68 backrake (click above to open LifeViewer)
Catagoluehere

The most common linear growth pattern is a 32c/68 orthogonal double T-ship backrake, as shown on the right. The shorter gap between adjacent T-ships is 20 ticks, while the longer gap is 112 ticks. It is the basis of many other linear growths collected in Catagolue, where the outputs are filtered by oscillators or crashed into other objects. The smallest linear growth polyplet predecessor is 3o$bo$bo$bo$2bo!, producing two opposite copies of this backrake with only 7 cells. Other ways to form the backrake include a collision between two copies of cloverleaf or w-pentomino (essentially the 3-tick descendant of 3o$bo$3bo!). The backrake is repeatedly generated and extinguished in some high-period oscillators such as the two p408 and the p828, and it can be reflected 180-degrees to make a p670 shuttle.

The third most common one is a 14c/92 diagonal puffer arising from a double interaction between a cloverleaf and a Julia, making the outputs solely Julias. Inrerestingly, these can be burnt at exactly the same speed, leading to a natural linear growth with the highest occured period.

x = 61, y = 51, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 45b3o$46bo2$46bo2$7bo13bo$5bo3bo9bo3bo2$7bo13bo$5bo3bo9bo3bo$6bobo11bo bo$7bo13bo$5bo3bo9bo3bo$7bo13bo$7bo13bo$2bo4bo4bo3bo4bo4bo$5bo3bo4bo4b o3bo$obo9bobobo9bobo$6b3o5bo5b3o3$4bo5bo7bo5bo$36b3o15b3o$36bobo15bobo $22b3o12bo17bo$23bo13bo17bo$23bo13bo17bo$22b3o10bo3bo13bo3bo$5bo7b3o 20bobo15bobo$4b3o6b3o5bobobo$4b3o7bo6bobobo10bobo15bobo$23bo11b5o13b5o $4b3o15b3o11b3o15b3o$4bobo16bo13bo17bo$5bo$4bobo48bo$55bo$54b3o$16bo 38bo$13bob2o29bo7b3o$16bo28b3o7bo$26bo18b3o$23bob2o28bo$26bo26b2ob2o$ 36bo$33bob2o$36bo15b3ob3o$46bo3b3ob3ob3o$43bob2o3bo2bo3bo2bo$46bo3bo3b obo3bo$51b3o3b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART GPS 10 ZOOM 8 THUMBSIZE 2 WIDTH 600 HEIGHT 480 Y 4 TRACK 0 -3/20 LOOP 120 ]]
7-engine p120 3c/20 forerake
(click above to open LifeViewer)

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 arising from symmetric soups.

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

Combining 3c/20 spaceships gives T-ship backrake, siderake and forerake of multiple periods. On the right is a forerake composed of a 2-engine p20 backrake by FWKnightship, a 2-engine 90-degree (back-to-side) reflector, and a p120 core sustained by a single dot spark.

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. A naturalistic primer was constructed by FWKnightship.

Signal Circuits

For demonstrations of this part, refer to the oscillator stamp collection above.

Oscillating

Giving off similar century-like sparks, the oscillators cloverleaf, Julia and butterfly could be excellent for periodic technologies. For Julia, T-ship 90-degree reflector, 180-degree reflector, Heisenburp (cf. p56 #9) and AND gate were found early on. However, later research focused on stable technologies and so p44 and p240 are lesser seeked.

Periodic 90-degree reflectors are also known with different mechanisms. Firstly, a head-on domino spark converts a bullet heptomino to a B-heptomino immediately, which can be turned to a new T-ship (type 4n+1) with a dot spark; this can be done at p8 (cf. p24 #5) with relatively tight bounding box, and the minimum working period for the domino sparker is p6 (cf. p18 #8). Secondly, the domino spark can be replaced with a xs12_2523ad2 (see below), providing new timing (but still type 4n+1) and thus allowing for p3 (cf. p27 #1) and p5 (cf. p30 #8) reflectors. Thirdly, bullet heptomino hitting a dying spark of 2×3 rectangle on the symmetrical axis gives another spark resembling Life's traffic light sequence, which evolves into a T-ship (type 4n+3) if suppressed with a tub (cf. p25 #5 and p34 #5).

There are a number of T-ship shuttles with periodic 180-degree reflectors (cf. p16 #2, p22, p24 #3, p30 #4, p33 #2, p36 #2, p40 #6, p48 #2).

A somewhat general gun construction scheme exists for oscillators emitting the 2×3 rectangle spark. Two copies of them face-to-face can make a blinker, and a third one dots its edge to create a T-ship. (cf. p30 #3) Another method involves dotting a "power button" blinker directly and using the resulting T-ship to regenerate original blinker as well as emitting another T-ship. (cf. p41 #3, p63 #4, p70, p124 #2; also see the p120 forerake above) This can also function as a parity-specific Heisenburp device for edgy dot-producing spaceships.

A decent application of periodic technologies is FWKnightship's p36960 OTCA metapixel, released surprisingly in January 2022.

Stable

Table 1: a brief summary of key repeat times

Item Repeat time in ticks
B-heptomino loop without extra signals 27
B-heptomino loop with extra T-ship 34
B-heptomino loop with extra B-heptomino 34
T-to-B converter 41
90-degree T reflector 41
T duplicator 41

Table 2: catalysts

Pattern Description Example
Tub Development of stable technologies uses tub as rock extensively. Many
Boat * As a replacement of tub when it loses one cell and becomes a t-tetromino;
* The first known bait for a T-ship giving two B-heptominoes at repeat time 51.
* p3 #3, p40 #5, p66 #2, p126 #1, etc
* p51 #2, p59 #5, p66 #3, p142 #1
Ship Its two-cell surface bites another two-cell surface via B4i, most commonly applied to a century spark to get a blinker; can be substituted with a tub at tub. p41 #3, p109 #1, p124 #2, p133 #4
Barge A flintstone that, upon hitting certain patterns, two B-heptominoes emerge like boat. p23 #1, p32 #1, p56 #1, p64 #2, etc
Beehive at tub A eater that works like CGoL fishhook, using the side near the tub; can be substituted with a xs8_2da3. p3 #13, p46 #5, p56 #7, p68 #2
Snake * As a replacement of tub, but cells connected to it survive longer; can be substituted with a fishhook for better clearance;
* A rock that works as in CGoL; can be substituted with a beehive.
* p16 #3, p43 #1, p84 #2, p92 #1, etc
* p23 #3, p38 #1, p56 #2
Domino at tub * As a replacement of tub when it gains one extra cell to be a boat;
* Providing a two-cell obo! surface, like CGoL hook with tail. More or less equivalent to a snake in some cases.
* p28 #8, p30 #7, p34 #1, p92 #3, etc
* p5 #24, p6 #6, p15 #2, p40 #3, etc
Boat at tub As a replacement of tub when it loses one cell and becomes a triplet spark. p43 #2, p48 #1, p55, p56 #8, etc
xs12_2523ad2 The core of second-phase development, with very robust reaction site. Many
xs16_at26z9m9 or xs17_2da32da23 A modified version of xs12_2523ad2 serving as the initial catalyst of T-to-B at repeat time 41. p41 #4, p82 #4, p97
xs10_5rkc The initial catalyst of T-ship reflector at repeat time 43. p43 #1
xs20_2da32523ad2 A dimerized version of xs12_2523ad2 but less robust. p10 #1, p38 #2, p40 #2, p78 #1, etc

Stable technologies are of particular interest. Concentrating on tubs and boats, the first-phase elaboration has 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. In the second phase starting from June 2021, much more catalysts were manually designed and tested against reactions, boosting development of the rule generally. As an example, the most compact 90-degree T-ship reflector uses a single 23-cell still life, which fits in a 12×15 bounding box and has a repeat time of 44 ticks, as shown in p44 #8.

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 10 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.

In January 2022, a fangtian (Chinese: 方田) has been completed that is the counterpart of p1 megacell in this rule, with a unit cell size of 8192×8192 and a recommended period of 262144 (218). Next month, a 327680×327680, period-16777216 (224) fangtian-2 extended the simulatable range to anisotropic range-1 3-state rules on a square grid. Both have a couple of sample patterns registered in Golly's collection under Patterns/HashLife/Metacell folder.

See also

Notes

  1. Taking the hundreds of thousands of combinations of cloverleaves that apgsearch does not separate into account, it is overwhelmingly more than the T-ship.
  2. This two-cloverleaf p480 is almost strictly volatile if it were not including two cells that turn on once per 240 ticks; check Oscillizer for that.

References

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

External links