Geometries of Two Spaceship Collisions in OCA

[GUYTU6J]

After seeing a misused collection here, I decide to make this thread. Here we will list the geometries of two-spaceship collisions, where the spaceship is small and common. I may crosspost the results to my Lifewiki userspace.
For example, this is a collection of 71 glider collisions in Game of Life, sorted by input path and direction:

Code: Select all

x = 364, y = 122, rule = B3/S23
2bo18bo17bo16bo16bo125bo20bo20bo17bo18bo14bo15bo15bo17bo16bo$bo18bo17b
o16bo16bo125bo20bo20bo17bo18bo14bo15bo15bo17bo16bo$b3o16b3o15b3o14b3o
14b3o123b3o18b3o18b3o15b3o16b3o12b3o13b3o13b3o15b3o14b3o5$b3o17b3o16b
3o15b3o15b3o$bo19bo18bo17bo17bo108b3o20b3o20b3o17b3o17b3o13b3o14b3o14b
3o16b3o15b3o$2bo19bo18bo17bo17bo109bo22bo22bo19bo19bo15bo16bo16bo18bo
17bo$186bo22bo22bo19bo19bo15bo16bo16bo18bo17bo16$327bo16bo16bo$2bo18bo
16bo17bo17bo251bo16bo16bo$bo18bo16bo17bo17bo252b3o14b3o14b3o$b3o16b3o
14b3o15b3o15b3o6$b3o17b3o15b3o16b3o16b3o239b3o16b3o16b3o$bo19bo17bo18b
o18bo243bo18bo18bo$2bo19bo17bo18bo18bo241bo18bo18bo15$261bo18bo14bo15b
o15bo17bo16bo$5bo17bo17bo16bo16bo13bo12bo17bo14bo124bo18bo14bo15bo15bo
17bo16bo$4bo17bo17bo16bo16bo13bo12bo17bo14bo125b3o16b3o12b3o13b3o13b3o
15b3o14b3o$4b3o15b3o15b3o14b3o14b3o11b3o10b3o15b3o12b3o6$bo18bo18bo17b
o17bo14bo13bo18bo15bo$2o17b2o17b2o16b2o16b2o13b2o12b2o17b2o14b2o$obo
16bobo16bobo15bobo15bobo12bobo11bobo16bobo13bobo109b2o18b2o14b2o15b2o
15b2o17b2o16b2o$249bobo17bobo13bobo14bobo14bobo16bobo15bobo$251bo19bo
15bo16bo16bo18bo17bo16$201bo19bo18bo20bo18bo14bo15bo15bo17bo16bo$6bo
17bo17bo16bo16bo13bo12bo16bo14bo64bo19bo18bo20bo18bo14bo15bo15bo17bo
16bo$5bo17bo17bo16bo16bo13bo12bo16bo14bo65b3o17b3o16b3o18b3o16b3o12b3o
13b3o13b3o15b3o14b3o$5b3o15b3o15b3o14b3o14b3o11b3o10b3o14b3o12b3o7$2bo
18bo18bo17bo17bo14bo13bo17bo15bo$b2o17b2o17b2o16b2o16b2o13b2o12b2o16b
2o14b2o44b2o20b2o19b2o21b2o18b2o14b2o15b2o15b2o17b2o16b2o$bobo16bobo
16bobo15bobo15bobo12bobo11bobo15bobo13bobo44b2o20b2o19b2o21b2o18b2o14b
2o15b2o15b2o17b2o16b2o$184bo21bo20bo22bo19bo15bo16bo16bo18bo17bo14$7bo
16bo17bo16bo16bo14bo12bo16bo14bo15bo$6bo16bo17bo16bo16bo14bo12bo16bo
14bo15bo176bo15bo17bo$6b3o14b3o15b3o14b3o14b3o12b3o10b3o14b3o12b3o13b
3o173bo15bo17bo$327b3o13b3o15b3o7$2b2o16b2o17b2o16b2o16b2o14b2o12b2o
16b2o14b2o15b2o$2bobo15bobo16bobo15bobo15bobo13bobo11bobo15bobo13bobo
14bobo160b2o16b2o18b2o$2bo17bo18bo17bo17bo15bo13bo17bo15bo16bo163b2o
16b2o18b2o$319bo17bo19bo!

The collection applies to almost all the rules with that evolutionary sequence of the glider. For rules with B2n, there are (at least) six additional geometries:

Code: Select all

x = 125, y = 14, rule = B2n3/S23
bo33bo19bo32bo15bo18bo$o33bo19bo32bo15bo18bo$3o31b3o17b3o30b3o13b3o16b
3o6$20b3o$6bo15bo$5b2o14bo98b2o$5bobo43b2o17b2o28b2o19b2o$50bobo18b2o
28b2o17bo$52bo17bo29bo!

If the rule is without B3q, this becomes a non-collision:

Code: Select all

x = 14, y = 8, rule = B3-q/S23
$4bo$4b2o3bo$3bobo3bobo$9b2o!

Another example is this half-sorted (EDIT:sorted now) collection of 29 p2 c/2 T ship collisions.

Code: Select all

x = 361, y = 83, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
3bo4bo34bo5bo33bo5b2o51bo30bo30bo30bo30bo30bo30bo30bo$ob2o4b2obo28bob
2o5b2obo27bob2o4b3o$3bo4bo34bo5bo33bo5b2o51bo30bo30bo30bo30bo30bo30bo
30bo$141b3o28b3o28b3o28b3o28b3o28b3o28b3o28b3o5$143bo29bo29bo29bo29bo
29bo29bo29bo$140bob2o26bob2o26bob2o26bob2o26bob2o26bob2o26bob2o26bob2o
$143bo29bo29bo29bo29bo29bo29bo29bo9$8bo40bo39b2o$3bo4b2obo31bo5b2obo
30bo4b3o$ob2o4bo31bob2o5bo30bob2o5b2o$3bo39bo39bo16$8bo40bo39b2o$8b2ob
o37b2obo35b3o$3bo4bo34bo5bo33bo5b2o51b3o28b3o28b3o28b3o28b3o28b3o28b3o
$ob2o36bob2o36bob2o58b3o28b3o28b3o28b3o28b3o28b3o28b3o$3bo39bo39bo59bo
30bo30bo30bo30bo30bo30bo5$143bo29bo29bo29bo29bo29bo29bo$140bob2o26bob
2o26bob2o26bob2o26bob2o26bob2o26bob2o$143bo29bo29bo29bo29bo29bo29bo8$
8bo40bo39b2o$8b2obo37b2obo35b3o$8bo40bo39b2o$3bo39bo39bo$ob2o36bob2o
36bob2o$3bo39bo39bo14$8bo80b2o$8b2obo76b3o$8bo80b2o2$3bo79bo$ob2o76bob
2o$3bo79bo!

EDIT: good point with the scripts, @LaundryPizza03. This post is intended to provide the results, which can adapt to appropriate rules by simply changing the rulestring.
FWKnightship's c/5 T ship collision collection, unsorted:

Code: Select all

x = 303, y = 247, rule = B37e/S2-in34i
242bo40bo14bo$202bo10bo28b2o8bo14bo15b2o13b2o$23bo13bo149bo14b2o9b2o
27bo9b2o13b2o14bo14bo$23b2o12b2o18bo15bo16bo58bo25bo11b2o13bo10bo11bo
26bo14bo$23bo13bo19b2o14b2o15b2o25bo31b2o11bo12b2o10bo37b2o$57bo15bo
16bo10bo15b2o16bo13bo12b2o11bo49bo$101b2o14bo17b2o25bo94bo43bo$101bo
33bo120bobo29b3o9b3o$120bo153bo13b3o$119bobo16bo55bo61b3o14b3o13bo$44b
o15bo32bo9b3o32bo25b3o11bo15bo10bo$25b3o15b3o14bo14b3o14b3o8b3o13b3o
15bobo25bo11b3o13bobo9bo10bo14b3o10b3o$26bo32bobo14bo27bo50bo9bo38bobo
8b3o14bo12bo$26bo49bo61bo15bobo37bo37bo12bo$60bo144bo$154b3o7$36bo$24b
3o8b3o9bo$25bo9b3o$46bobo53bo62bo11b3o$47bo31b3o9b3o7b3o7b3o34b3o13b3o
22bo$47bo17b3o12bo11bo8b3o34bo10bo14b3o10bobo8b3o11bo$66bo44bobo24bo
39bo9b3o11bo21b3o8bo28bo$112bo10bo13b3o61b3o8b3o10bo24bo13bo$123bo89bo
20bobo12b3o11b3o9b3o$122b3o110bo13b3o24bo$235bo5$69bo14bo8bo9bo22bo$
68b3o12b3o6b3o7b3o8bo11b3o$112b3o24bo$27bo10bo99b3o$26b3o8b3o$49bo$48b
3o101bo15bo9bo$151b3o13b3o7b3o9bo$188b3o11bo10bo11bo$201b3o8b3o9b3o41b
o11bo$238bo15bo12b3o9b3o$237b3o13b3o3$132b3o$133bo5$76bo2$75bobo$76bo$
76bo2$26bo19bo$26b2o18b2o14bo$26bo19bo15b2o$62bo2$134b3o$135bo$135bo$
29bo19bo14b3o$28bobo18bo14b3o$48bobo14bo$28b3o$49bo$80bo108bo$79b3o$
188bobo$189bo$189bo14$26bo$26b2o161bo$26bo161b3o8$28b3o$28b3o$29bo3$
260b3o2$260bobo$261bo3$196bo21bo18bo$196b2o20b2o17b2o$196bo21bo18bo4$
198b3o$198b3o$199bo40bo$221bo17b3o$220b3o$31bo$3bo27b2o232bo$3b2o12bo
13bo12bo219b3o$3bo13b2o25b2o$17bo26bo5$5b3o11b3o$5b3o12bo13bo$6bo13bo
13bo$33bobo10b3o$47bo$34bo12bo5$177bo2$176bobo$161bo15bo$147bo13b2o14b
o$147b2o12bo$147bo2$164bo$150bo12bobo$o148b3o$2o161b3o$o$178bo$177b3o$
3bo$3bo$2bobo2$3bo16$181b3o$182bo3$163bo$148bo14b2o$2bo145b2o13bo$2b2o
144bo$2bo2$150b3o$151bo14bo$151bo13bobo2$165b3o$4b3o$4b3o174bo$5bo174b
3o28$261b3o2$152b3o27b3o33bo42bobo$183bo34b2o42bo$152bobo63bo$153bo
138bo$292b2o$292bo4$221bo73bo$220bobo72bo$294bobo$220b3o$295bo3$185bo
78bo$184b3o76b3o$156bo$155b3o!

[LaundryPizza03]

Is there a script to automate the compilation of two-ship collisions? That would work for any two ships (and maybe oscillators) in every rule.

In general, there are always two types of collisions for two orthogonal or two diagonal ships: perpendicular collisions, and antiparallel collisions.

For identical oblique ships, the symmetry breaking means that there are six distinct angles for collisons:

1. Orthogonal acute, where the ships intercept at an acute angle and the sum of their velocities is orthogonal;
2. Diagonal acute, where the ships intercept at an acute angle and the sum of their velocities is diagonal;
3. Perpendicular;
4. Orthogonal obtuse, where the ships intercept at an obtuse angle and the sum of their velocities is orthogonal;
5. Diagonal obtuse, where the ships intercept at an obtuse angle and the sum of their velocities is diagonal; and
6. Antiparallel.

Code: Select all

#C Six collision angles for two copies of a (2,1)c/5 ship.
x = 93, y = 38, rule = B3-cnry4-acery5i/S23-a4-jknqr5y8
bo25bo$b2o22b3o$2o24bo$5bo$7bo83bo$9bo18bo61b2o$11bo79b2o$9bo19bo57bo$
7bo77bo$5bo24bo52bo$2o49bo29bo$b2o28bo17bo3bo25bo$bo27bo17bo7bo21bo$
27bo17bo11bo17bo$25bo14b2o19b2o7b2o$20b2o19b2o17b2o9b2o$21b2o18bo19bo
9bo$21bo3$7bo47bo$5b3o47b3o$6bo49bo3$bo6bo45bo$b2o$2o7bo43bo$5bo$7bo2b
o41bo$9bo$11bo39bo$49bo$47bo$45bo$40b2o$41b2o$41bo!

For an orthogonal and a diagonal spaceship, there are again two types of collisions, but at 45 and 135 degrees. And for an orthogonal or a diagonal ship colliding with an oblique ship, there are four, which can roughly be qualified as minor acute, major acute, minor obtuse, and major obtuse.

Code: Select all

#C Four collision angles for the same (2,1)c/5 ship and a c/2o ship.
x = 91, y = 13, rule = B3-cnry4-acery5i/S23-a4-jknqr5y8
35bo27bo$33b3o27b3o$2bo31bo29bo$2b2o$b2o$6bo29bo25bo26bo$8bo79b2o$10bo
26bo23bo27b2o$12bo72bo$14bo23bo21bo22bo$2b2o12bo12b2o18b2o18b2o10bo$o
2bo2bobobobobobobo8bo2bo2bobobobo7bo2bo2bobobobo7bo2bo2bobobobo$2b2o
25b2o18b2o18b2o!

Finally, for two oblique ships with different directions, all eight directions of one with respect to the other are distinct angles of collisions.

[praosylen]

It's worth noting that the above isn't quite accurate for asymmetric orthogonal or diagonal ships — there will typically be around twice as many collisions (and types of collisions) as for symmetric orthogonal/diagonal ships.