OCA:Bosco's Rule

Bugs
x=0, y = 0, rule = R5,C2,S33-57,B34-45,NM ! #C [[ THEME Fire ]] #C [[ RANDOMIZE2 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)
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).

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

Patterns

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.

Oscillators

Some p2, p3, p4, p5, p7 oscillators are known in Bugs.

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 6x6 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 ]]

Bosco (click above to open LifeViewer) Catagolue: here

Bosco with two blocks, period 284

Spaceships

Bugs 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.

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. Spaceships streams of smaller periods, e.g. 83 or 142, can be constructed by stacking two of more guns in a sequence.

A gun

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

Signal logic

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

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 Bugs, 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.

Bugs 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