Life Objects Buildable With 2 Gliders

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

The 71 different ways of colliding 2 gliders

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 on block B hept- omino Blinker Death Traffic light and glider Death Death Death Death Blockade (via Lumps of muck) Blinker Traffic light Block Death Death Death Traffic light Glider Loaf and blinker Inter- change Death Honey- farm Pond Death Honey- farm Honey- farm Tear- drop Loaf and tub and block and blinker Eater Block Death Beehive 2-glider mess Two blocks offset (4, 1) Pi hept- omino Pi hept- omino Block Loaf and blinker Death Death B hept- omino Block Four skewed blocks Death Pond Glider Block Death Death B hept- omino Pi hept- omino Traffic light Death Death Honey- farm Blinker Boat Death Death Death Loaf Death Death Death Death 2-glider oct- omino Honey- farm Block Death Death Death

The 1 spaceship buildable from 2 gliders

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.

The 11 small constellations buildable from 2 gliders

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

The top 7 naturally-occurring objects buildable from 2 gliders

 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.