All | Still-lifes | Pseudo-still-life | P2 oscillator | Spaceship | Constellations | Methuselahs | Naturally-occurring objects

The results of all 2-glider collisions have were explored in the 1970s, so these lists are known to be complete.

Collisions of 2 gliders can be arranged into two groups: 90-degree collisions, and 180-degree collisions.

The 90-degree collisions can be categorized by two factors: parity and phase. Since each glider moves one space every cycle, when both gliders move, they move 2 spaces relative to each other, so any separation can be reduced to modulo 2. Since the glider always occupies a 3x3 box, and is influenced by a 5x5 box, it is easy to show that two gliders will definitely miss if one is 20 generations (i.e. 5 cells) ahead of the other or more, and they will definitely hit if the separation is 18 generations or less. It just so happens that 19 generations also misses. This yields 2×19=38 90-degree collisions.

The 180-degree collisions can be categorized by two factors: separation and phase. Since the gliders are moving along parallel glide paths, parity is subsumed by phase. Since gliders move 2 spaces relative to each other each cycle, there are 8 possible phase differences. However, since the gliders are both the same, there is no distinction between which glider is "ahead", so these fold down to 4 (i.e. 0-4 are unique, but 5-7 are the same as 3-1). Furthermore, if the gliders are on the same glide path, there is no difference between left and right, so these 4 fold down to 2 (i.e. 0-2 are unique, but 3-4 are the same as 1-0). Since the glider is influenced by a 5x5 box, but moves orthogonally and flips every 2 generations, its stream of influence is a diagonal strip 8 cells wide, so streams with a separation of 0-6 cells will hit. (Streams 7 cells apart share neighbors, but since Life does not support birth on two neighbors, such streams pass each other harmlessly). This yields 7×5-2=33 180-degree collisions.

This is a table of all 71 2-glider collisions. The top two pairs of rows show odd- and even-separation 90-degree collisions, with phase differences from 0-18. The bottom 4 rows respectively show 5 180-degree collisions each from separations 6-5, 4-3, 2-1, and 0 cells. The results are indicated in color. These collisions can yield one of 23 possible results.

- Death is shown in white.
- Still-lifes are shown in green.
- Constellations are shown in yellow.
- Methuselahs are shown in red.
- Oscillators are shown in pink.
- Pseudo-still-lifes are shown in teal.
- Spaceships are shown in blue.

Block [2] | Boat [2] | Beehive [2] | Loaf; Burloaf [2] | Eater; Eater-1; Fishhook [2] | Pond [2] |

Block on block; Bi- block [2] |

Blinker [2] |

Glider; Feather- weight space- ship; FWSS [2] |

The Glider has a period of 4 and a diagonal velocity of *c*/4.
It moves one cell up and flips diagonally every two generations, effectively
moving one cell up and left every 4 generations.
It is the simplest and most common spaceship
in Life, and forms the basis for all syntheses.

Two blocks offset (4, 1) can eat a LWSS

Blinker [2] (3.038) | Block [2] (3.094) | Beehive [2] (5.230) | Loaf; Burloaf [2] (16.79) | Boat [2] (18.27) | Pond [2] (86.78) | Eater; Eater-1; Fishhook [2] (5756) |

**Other costs:**
2 gliders,
3 gliders,
4 gliders,
5 gliders,
6 gliders,
1 glider/bit,
>1 glider/bit,
unknown.

**See also:** Life objects sorted by:
counts,
frequency of occurrence,
cost in gliders,
name,
size in bits,
or type.

Copyright © 1997, 1998, 1999, 2013, 2014 by Mark. D. Niemiec.
All rights reserved.

This page was last updated on
*2015-02-19*.