OCA:Bosco's Rule

Bosco's Rule
x=64, y = 64, rule = R5,C2,S33-57,B34-45,NM ! #C [[ THEME Fire ]] #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
View static image
Rulestring	R5,C2,S33-57,B34-45,NM
Character	Chaotic

For the range-1 outer-totalistic rule, see OCA:Bugs (Life-like cellular automaton).

Bosco's Rule (also known as Bugs) is a Larger than Life cellular automaton, and perhaps one of the most studied such rules. The rule was devised by Kellie Evans. The name "Bosco's Rule" is derived from a sparky period-166 oscillator called "Bosco" (see Oscillators).

Patterns

Oscillators

Some p2, p3, p4, p5, p7 oscillators are known in Bosco's rule.

One particularly notable oscillator is a reflectorless flipping oscillator known as Bosco, oscillating at a period of 166. Its period can be increased by passing it near 6 × 6 blocks, with the period increasing to 284, 404, 520 and then by 118 for each extra pair of blocks. It is possible to construct oscillators with any multiples of these periods with loops of gun-based signal logic.

x = 12, y = 11, rule = R5,C0,S33-57,B34-45,NM 6bo$4b5o$2b5ob2o$b5o3b2o$b4o5bo$4o5b3o$b4o3b3o$b5ob4o$2b8o$3b7o$4b5o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 6 X -8 Y 16 GPS 32 AUTOSTART ]]

Bosco (click above to open LifeViewer) Catagolue: here

x = 48, y = 28, rule = R5,C0,S33-57,B34-45 4b3o$3b7o$2bo3b5o$bo5b4o$2o5b4o$b2o4b4o31b6o$b4o2b4o31b6o$2b8o32b6o$2b 7o33b6o$3b5o34b6o$4b3o35b6o12$6o$6o$6o$6o$6o$6o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 4 X 0 Y 3 GPS 48 THEME Book STARTFROM 284 ]]

Bosco with two blocks, period 284 (shown with highlighted envelope over one period) (click above to open LifeViewer)

Spaceships

Bosco's Rule is rich with many spaceships of various velocities, periods and directions. The most common are the orthogonal 5c/6, 8c/12, 4c/5, and the diagonal 8c/16, 23c/42. Other naturally occurring spaceships include orthogonal c/1 (many kinds), 2c/2, 6c/6, 7c/13; diagonal c/2, 2c/3, 5c/8, 6c/10; knightships (2,1)c/3, (1,2)c/4.

x = 28, y = 26, rule = R5,C0,M1,S34..58,B34..45,NM 8b5o$7b8o$6b2o2b5o$6bo4b5o$6bo4b5o$6b2o2b5o$7b8o$8b5o5$20b3o$20b4o$19b 7o$18b2o2b5o$3b3o11bo5b5o$2b6o8b2o6b4o$b9o7bo5b5o$2o3b5o8b2o2b5o$o4b5o 9b7o$o4b5o10b4o$2o3b5o10b3o$b9o$2b6o$3b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 GPS 24 AUTOSTART TRACKLOOP 660 528/660 0/660 ]]

A 174-cell orthogonal 528c/660 spaceship that looks like three spaceships; the interacting parts are two 5c/6 and one 4c/5 (click above to open LifeViewer) Catagolue: here

x = 26, y = 15, rule = R5,C0,M1,S34..58,B34..45,NM 4b2o$2b6o$b2o4b2o$b2o4b2o$4o2b4o$10o9b4o$b8o9b2o2b2o$b8o8b2o4b2o$b8o7b3o4b3o$ 2b6o8b4o2b4o$17b8o$17b8o$18b6o$18b6o$19b4o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 GPS 5 AUTOSTART TRACKLOOP 21 0/21 16/21 ]]

Two 5c/6 spaceships interact to form a 16c/21 spaceship (click above to open LifeViewer) Catagolue: here

Still lifes

The most common still life is the block, similar to its Life equivalent but as a 6 × 6 square as opposed to a 2 × 2.

The 6 × 6 block.
Catagolue: here

Other larger still lifes exist, often resembling thick hollow polygons.

Infinite growth

Multiple bug guns have been constructed using Boscos, with an example shown below. Periods other than 166 are possible to achieve by using boscos modified by pairs of blocks used as reflectors, splitters and eaters. It is possible to produce various kinds of spaceships by reacting another spaceship with each other or with boscos. Spaceship streams of smaller periods, e.g. 83 or 142, can be constructed by stacking two of more guns in a sequence.

x = 108, y = 59, rule = R5,C0,M1,S34..58,B34..45,NM 51b6o$51b6o$50b8o$50b8o$49b10o$49b3o4b3o$49b3o4b3o$50b2o4b2o$50b2o4b2o $51b6o$53b2o10$4b4o92b4o$3b6o90b6o$2b8o88b8o$b9o88b9o$5o2b4o86b4o2b5o$ 5o4b2o86b2o4b5o$b4o4bo88bo4b4o$b5o2b2o88b2o2b5o$2b4ob2o90b2ob4o$4b4o 92b4o19$10b5o78b5o$9b7o76b7o$9b8o74b8o$9b3ob5o72b5ob3o$8b3o4b4o70b4o4b 3o$8b2o5b4o70b4o5b2o$8b2o4b5o70b5o4b2o$9bo4b4o72b4o4bo$10bo2b4o74b4o2b o$11b4o78b4o$12bo82bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ MAXGRIDSIZE 9 THUMBSIZE 2 HEIGHT 640 WIDTH 960 ZOOM 6 GPS 20 AUTOSTART LOOP 167 ]]

A gun (click above to open LifeViewer)

The simplest known gun, discovered by Yoel Matveyev in 2002, is made from two reacting boscos.

The first natural occurrence of a gun happened in April 2023, in a soup submitted by Yoel Matveyev.

Signal logic

Reflectors, duplicators, eaters, period doublers, flip-flops, as well as various phase, location and type shifters of spaceships, have been constructed in Bosco's Rule.

Turing completeness

A so-called "rosary", finite version of Rule 110 was constructed by FWKnightship in February 2023, thus providing a somewhat weak proof of this rule's Turing completeness.

FWKnightship's design involves complex circuitry that relies on a mix of orthogonal 5c/6 and diagonal 8c/16 spaceships.

In less than a week later Yoel Matveyev independently posted his infinitely extending Rule 110 unit cells, which serve as a more rigorous proof.

Matveyev's design is conceptually similar to his Rule 110 tiles for FireWorld and Brian's Brain. It consists of AND-NOT gates, flip-flips and synchronization circuitry. The current state of each tile is stored in its one-bit memory (a toggle flip-flop).

Generalization

Higher-range outer-totalistic notation allows to define rules very similar to Bosco's Rule, but augmented with many additional still lifes, which can be used for easy construction of guns and oscillators of arbitrary periods, stable eaters, reflectors and duplicators, logic gates etc.

Bosco's Rule can be generalised to other ranges, such as the range-10 "Bugsmovie", the range-7 "Soldier Bugs" rule containing a p552 reflectorless rotating oscillator, and a range-6 rule containing a quadratic replicator.

Similarly shaped spaceships are also known in other ranges, starting from range-2 "Mini Bugs".

• 

  Dean Hickerson's period-552 reflectorless rotating oscillator.
  Catagolue: here

• 

  Dave Greene's 12-fold, period-46 version

External links

• MCell built-in Larger than Life rules: Bugs at Mirek Wójtowicz's Cellebration page
• Bosco's Rule at Adam P. Goucher's Catagolue