User:GUYTU6J/OCA:Glimmering Garden

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Glimmering Garden
熠熠种花
x=64, y = 64, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE2 THUMBLAUNCH THUMBNAIL THUMBSIZE 2 GRID ZOOM 6 WIDTH 600 HEIGHT 600 LABEL 90 -20 2 "#G" AUTOSTART PAUSE 2 GPS 8 LOOP 256 ]]
LifeViewer-generated pseudorandom soup
Rulestring 23-a4city6c7c/3-jknr4ity5ijk6i8
B3-jknr4ity5ijk6i8/S23-a4city6c7c
Character Chaotic

Glimmering Garden (Chinese name: 熠熠种花) is an isotropic non-totalistic 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. 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 has shown similar dynamics and engineering capabilities to Life in patterns.

Still lives

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

Power trio

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)
Catagolue: here
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)
Catagolue: here
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)
Catagolue: here

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$b3o! in Life. Without S4c in the rule, this pattern becomes a replicator wave. There is a common non-trivial dimer with smaller minimum population and a simple 7-cell predecessor b3o$obo$2o! (a century predecessor in Life).

Volatility status

Apart from the p240 cloverleaf, the p80 tri-cloverleaf and the p28 Julia, the following periods also have at least a strictly volatile oscillator respectively: 12 (two examples), 60 (twelve B-heptominoes stabilizing each other) and 152 (found in D4_+4).[note 2]

Apart from the p44 butterfly, the primitive periods for which statorless but not strictly volatile oscillator exists are 4, 14, 30, 86. Sufficiently sparky oscillators reflecting T-ships yield statorless oscillators at higher multiples of 12, 28, 30, 44, 80 and 86.

Collection

The rule has been known to be omniperiodic since July 2021, although for odd periods between 27 and 37 inclusive there is no oscillator that does not utilise spark interaction or signal circuitry.

#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 = 2605, y = 1312, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 15bo2bo16bo5b2o5bo5b2o12b2o4b2o4bo5b2o7b2o5b2o6b2o3b2o44bo2bo10bo2bo2b o37b2o20b2o88bo2bo2bo7bo2bo2bo18bo52bo77bo5bo7bo2bo2bo23b2o6bo19bo46bo 60bo2bo2bo7bo5bo28bo34bo105bo2bo2bo7bo2bo2bo155bo2bo10bo2bo2bo7bo2bo 32bo2bo26b2o84bo2bo10bo2bo2bo7bo2bo2bo35bo28b2o69bo2bo10bo5bo7bo2bo2bo 25bob2o45b2o6bo72bo2bo10bo2bo2bo7bo2bo2bo29b2o114bo2bo2bo7bo2bo2bo7bo 2bo2bo145bo2bo2bo7bo2bo2bo7bo2bo2bo29bo125bo2bo2bo7bo2bo2bo7bo2bo2bo 165bo2bo2bo7bo5bo7bo2bo2bo155bo2bo2bo7bo2bo2bo7bo2bo2bo$14bob2obo14bob o3bobo4bobo3bo2bo2b2obo3bo2bo3bobo3bob2o3bobobo3bo2bo5bobo4bo5bo43bob 2obo8bob2ob2obo36bobo20bo87bob2ob2obo5bob2ob2obo16bobo11bo20bo17bobo 75bobo3bobo5bob2ob2obo23bo5bobo17bobo44bobo58bob2ob2obo5bobo3bobo26bob 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o2bo5bobo$243b3o2b2o16bob3obo93b2o3bobo11b2obo17b2o$244bo3bo18bo3bo92b obo5bo12bo$244b2obo19b2o95b2obo3bo801bo$244bobobo117bo805bobo$244b2ob 2obo922bo4bo$246bo2b2o122bo803bobo12bo$245b2o126b3o800bobo12bobo$376bo 800bo14bo$375b2o$1180bo$1179bobo$1180bo2$2417b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 1500 HEIGHT 900 ZOOM 0.5 ]]
Stamp collection for 16 still lives and 911 oscillators (period＜1000) as of February 15, 2023
(click above to open LifeViewer)
RLE: here Plaintext: here

Spaceships

The glider from Life does not work in this rule. Spaceships from official apgsearch symmetries are listed below:[note 3]

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, xq12_gggxcqre4w4erqcxgggz05yg5 and xq12_y2gom3as88sa3mogz1b1yg1b1 Two T-ships escorting two B-heptominoes, from even bilateral symmetries
(18,0)c/36 xq36_yt..
(24,0)c/48 xq48_37... and xq48_y3...
(36,0)c/72 xq72_y2...
(36,0)c/72 xq72_ya.. Four B-heptomino in a row
(48,0)c/96 xq96_yag..., xq96_37s..., xq96_y42..., xq96_yzy..., xq96_y44... Two B-heptomino pair puffers in a line; the first one is the minimal form
(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. See section below for details
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 THUMBSIZE 4 GPS 10 TRACK 7/46 -7/46 ZOOM 8 X 2 Y 4 WIDTH 720 HEIGHT 720 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 THUMBSIZE 4 GPS 2 TRACK -0.25 -0.25 ZOOM 8 WIDTH 720 HEIGHT 640 LOOP 4 ]]
A 250-cell c/4 diagonal spaceship
(click above to open LifeViewer)
Catagolue: here

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 = 153, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c o4bo3bobo3bobobo2bo3bo3bo3bo4bo4bobo33bo5bo3bo3bobo4bobo$154bobobo$obo 2bo2bo3bo4bo4bo3bo3bo3bobo2bo2bo37bobobobo3bo2bo6bo3bo$156bo$o2bobo2bo 3bo4bo4bobobo3bo3bo2bobo2bo2bobo32bo2bo2bo3bo3bobo3bo$156bo$o4bo2bo3bo 4bo4bo3bo3bo3bo4bo2bo4bo32bo5bo3bo6bo2bo3bo$156bo$o4bo3bobo5bo4bo3bo3b o3bo4bo4bobo33bo5bo3bo3bobo4bobo$156bo10$9bo4bo144bo5b2o$6bob2o4b2obo 138bob2o4b3o$9bo4bo26bo117bo5b2o$92bo$41bo$40b3o49bo$91b3o3$14bo$9bo4b 2obo21bo$6bob2o4bo21bob2o49bo$9bo29bo46bob2o$89bo73b3o$163b3o$164bo3$ 14bo$14b2obo$9bo4bo144bo$6bob2o146bob2o$9bo34bo114bo2$44bo$43b3o2$14bo $14b2obo$14bo$9bo29bo101bobobobobobobobobobobobobobobobobo$6bob2o26bob 2o$9bo29bo$89bo59bobobo3bobobo2bo2$89bo59bo4bo2bo6bo$14bo73b3o68bobo$ 14b2obo131bo4bo2bo6bo$14bo$149bobobo3bobobo2bobobo$9bo$6bob2o79bo$9bo 35bo40bob2o68bo$89bo$45bo112bo$44b3o110b3o4$15bo$9bo5b2obo20bo119bo$6b ob2o5bo20bob2o116bob2o$9bo29bo119bo6$15bo$15b2obo$9bo5bo$6bob2o$9bo 150bo$38b3o$38b3o119bo$39bo119b3o2$15bo$15b2obo$15bo$9bo29bo119bo$6bob 2o26bob2o116bob2o$9bo29bo119bo7$15b2o$9bo4b3o$6bob2o5b2o$9bo153bo$41b 3o$41b3o119bo$42bo119b3o3$15b2o$14b3o$9bo5b2o22bo119bo$6bob2o26bob2o 116bob2o$9bo29bo119bo2$90b3o$90b3o$91bo$15b2o$14b3o$15b2o$9bo$6bob2o 79bo$9bo76bob2o$42b3o44bo69b3o$42b3o114b3o$43bo116bo$15b2o$14b3o$15b2o 2$9bo29bo119bo$6bob2o26bob2o116bob2o$9bo29bo119bo11$44b3o$44b3o$45bo5$ 39bo$36bob2o49bo5bo$39bo46bob2o5b2obo$89bo5bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 4 HEIGHT 800 WIDTH 800 ]]
All 29 distinct two T-ship collisions
(click above to open LifeViewer)

The bullet heptomino is the smallest and fastest spaceship. Its speed is c/2 orthogonal. Its other phase is a t-tetromino with a 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).

xq4_nmkz31

x = 35, y = 19, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c 2o$3o$2o12b3o$14b3o$15bo$8bo$5bob2o21bo$8bo20bobo$15bo12bobo$14b3o12bo $2o12b3o$3o$2o18bo$19bobo$20bobo$21bobo9bo$22bo9bobo$33bo$33b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ZOOM 12 Y 3 AUTOSTART GPS 4 PAUSE 2 T 5 PAUSE 2 T 26 PAUSE 2 T 104 GPS 10 PAUSE 2 LOOP 105 HEIGHT 700 WIDTH 800 ]]
Synthesis and conversion of xq4_nmkz31
(click above to open LifeViewer)

This non-monotonic spaceship is made up of two hexominoes in one phase. It has a 5T synthesis that is intrinsically a T+blinker+two dots reaction, and it can be easily converted to T-ship or B-heptomino. A flotilla of three can escort a 15-cell pattern.

Infinite growth patterns

Infinite growth patterns of different growth rates are known.

Linear growth

The rule is inhabited by abundant linear growth patterns including 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 HEIGHT 600 WIDTH 600 ]]
The period-13 T-ship gun
(click above to open LifeViewer)
Catagolue: here
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)
Catagolue: here

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; this tends to slow down soup searches severely in D2_+1, D4_+1, D4_+2 and D8_1 symmetries. 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 occurred 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 signal circuits in this part, refer to the oscillator stamp collection above.

Oscillating

With power trio

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 #10) and AND gate were found early on. However, later research focused on stable technologies and so p44 and p240 are lesser seeked.

Notably, copies of Julia could be laid in a row such that their binary state-flipping emulates a replicator in Wolfram's Rule 60 (cf. p224), and copies of interlinked cloverleaf could emulate a certain chaotic, anisotropic 2-dimensional rule.[2]

General

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 #6) 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 #10) reflectors. Thirdly, bullet heptomino hitting a dying spark of 2×3 rectangle on the axis of symmetry 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 #6).

There are a number of T-ship shuttles with periodic 180-degree reflectors (cf. p16 #2, p22 #2, p24 #3, p30 #4, p33 #2, p36 #2, p40 #7, p48 #3, p76 #5).

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 #2, 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 minimum repeat times

Item Repeat time in ticks
B-heptomino loop without extra signals 27
B-heptomino loop with extra T-ship 27
B-heptomino loop with extra B-heptomino 27
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, p10 #13, 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 #3
Barge A flintstone that, upon hitting certain patterns, two B-heptominoes emerge like boat. p23 #1, p32 #1, p56 #1, p64 #2, etc
Beehive siamese tub An eater that works like CGoL fishhook, using the side near the tub; can be substituted with a xs8_2da3. p3 #13, p46 #7, p56 #12, 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 #9, p32 #4, p34 #1, p92 #3, etc
* p5 #26, p6 #3, p15 #2, p40 #3, etc
Boat siamese tub As a replacement of tub when it loses one cell and becomes a triplet spark. p43 #2, p48 #1, p55, p56 #9, 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 #5, 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 #8, p38 #2, p40 #2, p78 #4, 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.
  3. ↑ This list does not include xq24_yc..., a (12,0)c/24 spaceship that works but has not appeared in the census of this rule yet; it was originally found by FWKnightship in a rule with S6n.

References

  1. ↑ GUYTU6J (June 12, 2019). Re: Reflectorless Rotating Oscillators (RRO) (discussion thread) at the ConwayLife.com forums
  2. ↑ GUYTU6J (October 26, 2022). Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums

External links

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