User:Haycat2009/OCA:Determination

Determination
x=64, y = 64, rule = B2a3i/S12 ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE2 RANDSEED 1729 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	12/2a3i B2a3i/S12
Character	Explosive

Determination is a rule with rulestring B2a3i/S12. It is named such due to having B2a, yet having decent tech. It has a lot of technology dealing with moon, such as rakes, puffers and lasers.

Spaceships

Only photons of p2 and above are possible. The 1st time it leaves bounding box, it is unstoppable as there is a line of at least 2 and it will propagate forever.

The minimum period stream for photons is 7 due to sparks and the behaviour of it.

Tech

x = 70, y = 23, rule = B2a3i/S12 o8bo5bo8bo4bo8bo7bo6bo6bo8bo$bo6bo7bo6bo6bo6bo9bo4bo8bo6bo2$2bob2obo9b ob2obo8bob2obo9b2o4b2o8bo4bo$bo6bo7bo6bo6bo6bo11b2o10bo6bo$47bo4bo$16b o6bo3bo12bo5bo6bo7bo6bo$17bo4bo3bo14bo20bo4bo$2bo4bo$3bo2bo10bo4bo8bo 4bo25bob2obo$18bo2bo10bo2bo25bo6bo2$61bo6bo$62bo4bo2$62bo4bo$61bo6bo2$ 61bo6bo$62bo4bo2$62bo4bo$63bo2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

Guns. Last 2 are infinitely extensible (click above to open LifeViewer)

x = 10, y = 22, rule = B2a3i/S12 3bo2bo$4b2o4$o8bo$bo6bo2$2bo4bo$bo6bo8$o8bo$bo6bo2$2bo4bo$bo6bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

Bidirectional duplicator, creates 6 if moon is in dense phase as it enters or 2 if in sparse phase. (click above to open LifeViewer)

x = 6, y = 20, rule = B2a3i/S12 2bo2bo$3b2o$3b2o5$2bo2bo$3b2o9$bo$o4bo$4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

Period-agnostic eater. Yum! (click above to open LifeViewer)

x = 7, y = 19, rule = B2a3i/S12 3bo2bo$4b2o15$o$bo4bo$5bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

1 lane 180˚ reflector. Proves that oscs of p6+4n exist, n 0 or above. (click above to open LifeViewer)

x = 8, y = 10, rule = B2a3i/S12 3bo2bo$4b2o$o$bo3$7bo$6bo$3bobo$4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

Different duplicator, with 90 ˚ output (click above to open LifeViewer)

x = 8, y = 12, rule = B2a3i/S12 o$bo$3bo2bo$4b2o3$bo$o$bo5bo$6bo$3bo$4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

Produces 3 moons. (click above to open LifeViewer)

x = 10, y = 19, rule = B2a3i/S12 3bo2bo$4b2o11$2bo5bo$bo7bo3$o$bo4bo$5bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

180 degree reflector with different output parity from the duplicator above. (click above to open LifeViewer)

x = 14, y = 9, rule = B2a3i/S12 5bo$6bo2$13bo$bo10bo$o11bo$13bo$3bo4bo$2bo6bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

90 degree reflector based on duplicator. RT 14. (click above to open LifeViewer)

x = 7, y = 10, rule = B2a3i/S12 2bo2bo$3b2o5$bo$o$6bo$5bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

0 degree 1 lane shifter. RT 8. (click above to open LifeViewer)

x = 18, y = 6, rule = B2a3i/S12 17bo$16bo$16bo$17bo$bo4bobo2bo$o6bo2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

One-phase heisenburp found while trying to make a one-way tube. RT 7. (click above to open LifeViewer)

x = 8, y = 2, rule = B2a3i/S12 o2b2o2bo$b2o2b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

p2 rake. Weird but true! (click above to open LifeViewer)

x = 8, y = 8, rule = B2a3i/S12 o6bo$bob2obo$3b2o$3b2o$3b2o$3b2o$bob2obo$o6bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

Weird gun with high kinetic symmetry (click above to open LifeViewer)

x = 8, y = 12, rule = B2a3i/S12 o6bo$bo4bo5$bo$o3$3b2o$2bo2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

RT 12 replicator, can be used for RT 12 reflector. A merge circuit to top it off. (click above to open LifeViewer)

x = 6, y = 10, rule = B2a3i/S12 bo3bo$2b3o3$o$bo3$bo$o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

Converter (click above to open LifeViewer)

x = 58, y = 59, rule = B2a3i/S12 40bo2bo$41b2o28$30bo19bo6bo$31bo19bo4bo5$31bo4bo14bo$30bo6bo12bo11$37b o12bo6bo$36bo14bo4bo$o$bo$bo$o$31bo4bo19bo$30bo6bo19bo3$53b2o$52bo2bo ! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

Memory cell. Reading is easy. Inselting a signal can be done 4 ways (from the left in this example) Removing a signal is easy too, and at the top (click above to open LifeViewer)

Still-lifes

It can be proven that every polyplet SL in this rule is an SL in the rule B/S12V rotated 45 degrees.

PROOF: B2a3i allows every orthogonal line of cells to expand unless there is a stable covering covering the line. Hence all of the allowed moves are diagonal, hence, every polyplet SL in this rule is a SL in the rule B/S12V rotated 45 degrees.

The smallest non-polyplet SLs in this rule are these:

x = 15, y = 18, rule = B2a3i/S12 bo4bo7bo$o6bo5bo2$2o4b2o4b2o2$o5bo6bo$bo5bo4bo5$2bo5bo5bo$bo5bo5bo2$2o 4b2o4b2o2$bo4bo5bo$2bo2bo7bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

The smallest 6 nonpolyplet SLs in Determination. (click above to open LifeViewer)

Oscillators

Almost all oscillators are hasslers of an active region.

x = 15, y = 13, rule = B2a3i/S12 10bo$4bo6bo$3bo3$11bo$3bo8bo$2bo5b2o$5b2ob2o$5b2o7bo$o7bo4bo$bo4bo2bo $5bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

p11 hassler (click above to open LifeViewer)

x = 7, y = 10, rule = B2a3i/S12 3bo$4bo2$o2b2o$bo$5bo$2b2o2bo2$3bo$2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]

p2 on-off (click above to open LifeViewer)

Reflector-based

Assume n >= 0.

Using the reflectors, oscillators of every period 6+4n are possible.

x = 14, y = 61, rule = B2a3i/S12 2bo$bo$4bo$b2o2bo$2bo$o$bo$4bo$3bo5$2bo$bo$6bo$b2o4bo$2bo$o$bo$6bo$5b o5$2bo$bo$8bo$b2o6bo$2bo$o$bo$8bo$7bo5$2bo$bo$10bo$b2o8bo$2bo$o$bo$10b o$9bo5$2bo$bo$12bo$b2o10bo$2bo$o$bo$12bo$11bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

Some adjustable oscillators. (click above to open LifeViewer)

In addition, guns of every period 18+4n are possible.

x = 61, y = 9, rule = B2a3i/S12 7bo20bo21bo$6bo3bo16bo5bo15bo7bo$11bo22bo23bo$bobo8bo9bobo10bo8bobo12b o$o2bo9bo7bo2bo11bo6bo2bo13bo$bo10bo9bo12bo8bo14bo$2bo20bo21bo$3bo3bo 16bo5bo15bo7bo$6bo22bo23bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

Some adjustable guns. (click above to open LifeViewer)

W22

Below are oscillators using the W22 replicator, which is a domino enclosed in a stable covering.

x = 49, y = 190, rule = B2a3i/S12 14bo3bo$26bo$14bo3bo5bobobo$23bo5bo$14bobobo8bo$27bo$18bo4bo5bo$24bob obo$18bo7bo6$7bobo4bobobo$27bobobo$9bo8bo5bobobobo2bo$23bo10bo$9bo4bo bobo12bo$31bo$9bo4bo8bo10bo$24bobobobo2bo$7bobobo2bobobo8bobobo6$14bo bobo$27bobobo$14bo3bo5bobobobobobo$23bo11bo$14bobobo12bo$31bo$14bo3bo 4bo11bo$24bobobobobobo$14bobobo8bobobo6$14bobobo$27bobobobo$14bo9bobo bobobo2bo$23bo12bo$14bobobo9b4o$28b4o$18bo4bo12bo$24bobobobobo2bo$14b obobo8bobobobo6$7bobobo2bobobo$27bobobobo$11bo2bo3bo5bobobobobobobo$23b o13bo$7bobobo2bobobo16bo$35bo$7bo6bo3bo4bo13bo$24bobobobobobobo$7bobo bo2bobobo8bobobobo6$7bobobo2bobobo$27bobobobobo$11bo2bo9bobobobobobob obo$23bo15bo$7bobobo2bobobo13b4o$32b4o$7bo10bo4bo15bo$24bobobobobobob obo$7bobobo2bobobo8bobobobobo6$7bobo4bobobo8bobobobobobo$24bobobobobo bobobobo$9bo4bo8bo17bo$31bo3b3o$9bo4bobobo12bo3b3o$23bo17bo$9bo8bo5bo bobobobobobobobo$27bobobobobobo$7bobobo2bobobo6$7bobobo2bo3bo8bobobob obobobo$24bobobobobobobobo2bo$11bo2bo3bo4bo18bo$34b2o2bo$7bobobo2bobo bo15b2o2bo$23bo18bo$7bo10bo5bobobobobobobobo2bo$27bobobobobobobo$7bob obo6bo6$obo4bobobo2bo3bo8bobobobobobobobo$24bobobobobobobobobobobo$2b o8bo2bo3bo4bo21bo$43bo$2bo4bobobo2bobobo24bo$23bo21bo$2bo4bo10bo5bobo bobobobobobobobobo$27bobobobobobobobo$obobo2bobobo6bo6$7bobobo2bobobo 8bobobobobobobobo$24bobobobobobobobobobobo$7bo10bo4bo21bo$32bo4bo$7bo bobo2bobobo13bo4bo$23bo21bo$11bo2bo9bobobobobobobobobobobo$27bobobobo bobobobo$7bobobo2bobobo6$7bobo4bobobo8bobobobobobobobo$24bobobobobobo bobobobobo$9bo4bo8bo21bo$31bobo3bo3bo$9bo4bobobo12bobo3bo3bo$23bo21bo $9bo4bo3bo5bobobobobobobobobobobo$27bobobobobobobobo$7bobobo2bobobo5$ obo4bobobo2bobobo8bobobobobobobobobo$24bobobobobobobobobobobobo$2bo8b o6bo4bo23bo$35b4o3b3o$2bo4bobobo2bobobo16b4o3b3o$23bo23bo$2bo8bo2bo9b obobobobobobobobobobobo$27bobobobobobobobobo$obobo2bobobo2bobobo6$7bo bo4bobobo8bobobobobobobobobo$24bobobobobobobobobobobobo$9bo4bo3bo4bo23b o$34b2o3bob3o$9bo4bobobo15b2o3bob3o$23bo23bo$9bo8bo5bobobobobobobobob obobobo$27bobobobobobobobobo$7bobobo2bobobo6$7bobobo2bobobo8bobobobob obobobobobo$24bobobobobobobobobobobo2bo$11bo6bo4bo24bo$34bo3b3obo$7bo bobo2bobobo15bo3b3obo$23bo24bo$11bo6bo5bobobobobobobobobobobo2bo$27bo bobobobobobobobobo$7bobobo2bobobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 1024 WIDTH 768 ]]

Some oscillators using the W22 replicator. (click above to open LifeViewer)

Turing-completeness

It is easier to prove it by consructing a computer than by W110 stripe. An 8-bit programmable computer was made with a gun, eater, reflector and duplicator, all of which Determination has. Also, this is the third rule to be proven turing-complete by computer, after Conway Life and Eppstein.