2-glider collision
A 2-glider collision is a collision of two gliders at right angles or head-on.[note 1]
The gliders can react with each other in many different ways. A large number of the reactions cleanly destroy both gliders leaving nothing. Many of the remaining reactions cleanly create some common objects, and so are used as the first steps in glider syntheses or as part of constructing interesting objects using rakes. Only a small number of collisions can be considered dirty due to creating multiple objects or a mess.
Results
Below are tabulated possible results of a two-glider collision, along with how many distinct ways they can occur.
| Result | Right-angle | Head-on |
|---|---|---|
| nothing | 11 | 17 |
| Beehive | 1 | 0 |
| B-heptomino | 1 | 2 |
| Bi-block | 1 | 0 |
| Blinker | 2 | 1 |
| Block | 3 | 3 |
| Boat | 0 | 1 |
| Eater 1 | 1 | 0 |
| Glider | 1 | 1 |
| Honey farm | 3 | 2 |
| Interchange | 1 | 0 |
| Loaf | 0 | 1 |
| Lumps of muck | 1 | 0 |
| Two-glider octomino | 0 | 1 |
| Pi-heptomino | 2 | 1 |
| Pond | 1 | 1 |
| Teardrop | 1 | 0 |
| Traffic light | 2 | 1 |
| Four skewed blocks | 0 | 1 |
| Dirty | 6 | 0 |
The messiest of the two-glider collisions in the "dirty" category is 2-glider mess.
| All 71 distinct 2-glider collisions,[2][3] arranged by what they synthesize in a pattern constructed by Jason Summers[4] (click above to open LifeViewer) RLE: here Plaintext: here |
Classification of the results
In 1973, Everett Boyer et al. proposed a classification scheme for 90° two-glider collisions.[5] By considering the delay and parity of separation, a two-glider collision is labelled with a number and a plus/minus sign. For instance, in the collision that gives a bi-block, the paths of two gliders are separated by an odd number of cells (the effect can be seen clearly under LifeHistory), and two gliders arrive simultaneously to the intersection point of two paths — therefore it is labelled "0-". Delaying any of the two gliders gives a "1-" reaction that synthesizes a B-heptomino.
The results are tabulated below. A pair of colliding gliders has the same parity with an even delay (or different with odd ones), and has the same color with an even parity of separation (or different with odd ones).
| Delay | Parity of separation | |
|---|---|---|
| Even (+) | Odd (-) | |
| 0 | (0+) Interchange[note 2] | (0-) Bi-block[note 3] |
| 1 | (1+) 94-tick spark (Ghost Herschel / banana / domino) | (1-) B-heptomino |
| 2 | (2+) Honeyfarm | (2-) Blinker |
| 3 | (3+) Pond | (3-) 32-tick spark (Ghost Herschel / banana / domino) |
| 4 | (4+) 4-tick spark (obo! spark) | (4-) Traffic light and glider |
| 5 | (5+) Honeyfarm | (5-) 6-tick spark |
| 6 | (6+) Honeyfarm | (6-) 13-tick spark (P-pentomino / V spark / domino) |
| 7 | (7+) Teardrop | (7-) 10-tick spark (domino) |
| 8 | (8+) Blinker, loaf, block and tub[note 4] | (8-) 8-tick spark (domino) |
| 9 | (9+) Eater 1 | (9-) Lumps of muck |
| 10 | (10+) Block | (10-) Blinker |
| 11 | (11+) 4-tick spark (xp0_14) | (11-) Traffic light |
| 12 | (12+) Beehive | (12-) Block |
| 13 | (13+) Two-glider mess | (13-) 11-tick spark (P-pentomino / V spark / domino) |
| 14 | (14+) Half-blockade | (14-) 13-tick spark (V spark / domino) |
| 15 | (15+) House | (15-) 4-tick spark |
| 16 | (16+) Pi-heptomino | (16-) Traffic light |
| 17 | (17+) Block | (17-) Glider (90° kickback) |
| 18 | (18+) Blinker and loaf[note 5] | (18-) Blinker and loaf[note 5] |
| ≥19 | No reaction onwards | |
Another table of 180° collisions can be similarly made.
| Lane offset | Time offset | ||||
|---|---|---|---|---|---|
| 0 | 4 | 1 | 3 | 2 | |
| 0 | 4-tick spark (xp0_108) | 6-tick spark (xp0_106 / dot) | 6-tick spark (duoplet) | ||
| 1 | 10-tick spark | Block | 5-tick spark (banana / domino) | Honey farm | Two-glider octomino |
| 2 | 5-tick spark | 4-tick spark (domino) | 4-tick spark (domino) | 5-tick spark (domino) | Loaf (from V-pentomino or W-pentomino) |
| 3 | 4-tick spark (xp0_h) | 5-tick spark | Honey farm | Boat | Blinker (from Angel) |
| 4 | 5-tick spark | 12-tick spark | Traffic light | B-heptomino | Pi-heptomino |
| 5 | 3-tick spark | 8-tick spark | Pond | Block | Glider (180° kickback) |
| 6 | Four skewed blocks | 7-tick spark (domino) | Block | 12-tick spark (banana / domino) | B-heptaplet |
| ≥7 | No reaction onwards | ||||
See also
Notes
- ↑ The direction requirement is a necessary but not sufficient condition for the 2-glider collision to be valid. Two gliders moving in the same direction either never interact or collapse in at most 4 ticks due to being very close. In the latter case, the gliders cannot come from infinity and this "collision" is deemed invalid. Glider syntheses should avoid such glider pairs.[1]
- ↑ The two gliders can be reflected by a block, as shown in the rephaser and glider-block cycle article.
- ↑ This reaction can also be seen as a tagalong for a c/3 orthogonal dot sparker, as discovered by MathAndCode and wwei23.[6]
- ↑ Ash on Catagolue: here
- ↑ 5.0 5.1 Ash on Catagolue: here
References
- ↑ Bob Shemyakin (February 15, 2015). Errors of glider synthesis (discussion thread) at the ConwayLife.com forums
- ↑ Robert Wainwright (September 1972). Lifeline, vol 5, page 6.
- ↑ Mark Niemiec (February 25, 2021). Re: Thread For Your Accidental Discoveries (discussion thread) at the ConwayLife.com forums
- ↑ 71 Glider Collisions at Game of Life News. Posted by Dave Greene on January 29, 2005.
- ↑ Robert Wainwright (September 1973). Lifeline, vol 11, page 10.
- ↑ wwei23 (December 29, 2020). Re: Thread for your Trolls (discussion thread) at the ConwayLife.com forums
External links
- 2-glider collision at the Life Lexicon
- Life Objects Buildable With 2 Gliders at Mark D. Niemiec's Life Page