The 2D cellular automaton Game of Life determines whether a cell lives, dies or is born by counting the number of live cells in its eight neighboring cells. A living cell is represented by 1 and an empty cell by 0. An empty cell is born to a living cell if it has exactly three living neighbors. A living cell survives if and only if it has two or three neighbors. In shorter form, the Game of Life is B3/S23, encoded as rule 224 in the CellularAutomaton[] function. A cellular automaton rule is applied to an initial condition. If an initial condition does not change after application of the rule, it is known as a stilllife. If the initial condition repeats in the same position after more than one step, it is known as an oscillator. If the initial condition repeats in an offset position, it is known as a glider. One famous initial condition is ((1,1,0),(0,1,1),(1,0,0)) or , frequently known as "the Glider". In addition to the initial condition, a glider has a behavior as it is run by the repeated application of the cellular automaton. Here are four different gliders all starting with , along with the glider index and a rule giving that behavior. With the initial condition , the first row is generated by the Game of Life (B3/S23, rule 224) as well as HighLife (B36/S23, rule 4320), Coagulations (B378/S235678, rule 256224) and Stains (B3678/S235678, rule 260320). In all, the firstrow behavior is seen with 256 different rules, with minimum (B3/S23, rule 224) and maximum (B3678/S0235678, rule 260322). Below is a different initial condition with different behaviors, with an extra column for the horizontal offset. Note how row 4 below and rows 2–4 above seem to have a black background on even steps. Within the rules, giving black background behavior is B0, birth with zero neighbors, which causes the field to rapidly strobe between black and white, an effect suppressed in this Demonstration since it can trigger epilectic seizures. If a glider moves too fast, use "delay" to slow it down. A collection of different gliders in different rule systems is compiled at [1].
The data in [1] was modified in the following ways: 1. The first glider in [1], the Caterpillar, has a size {4195, 330721} that is too large to be shown here. The classic was substituted. 2. All gliders were reoriented to have displacement not going down or to the left. 3. The "smallest" 0background version of each glider was selected as initial condition. The largest widths and heights were also recorded. Some of the stranger gliders are the following: Knightgliders. The displacement goes up and to the right, moving like a chess knight. Glider indices: (582, 657, 1364, 1402, 1590, 1666, 1667, 1968, 2051, 2401). Exploders. The maximum size is much larger than the smallest size. Glider indices: (194, 739, 491, 751, 659, 223, 5402, 464, 226, 3469). Slow. These gliders have very high periods and small offsets. Glider indices: (13047, 6802, 9553, 6801, 10671, 1434, 9089, 11415, 9088, 12066). Longjumper. These gliders have a small size with a large offset. Glider indices: (13207, 3955, 3954, 5784, 4391, 12471, 8294, 5327, 13206, 13325). Certain famous cellular automaton rules have many gliders. Let "⟶" stand for "has gliders with these indices". Seeds (B2/S, rule 16) ⟶ (195, 230, 231, 2430, 11003, 13102, 17681, 18042, 18337, 21531, 21576). Life (B3/S23, rule 224) ⟶ (115, 1062, 9153, 10240, 11302, 13374, 13491, 13881, 14105, 16485, 16532, 17361, 18216, 18788, 19739, 21362). HighLife (B36/S23, rule 4320) ⟶ (115, 1062, 11302, 12056, 13182, 14006, 16573, 20154, 20416). Bacteria (B34/S456, rule 11072) ⟶ (3301, 11698, 12238, 14097, 16874). Move (B368/S245, rule 72288) ⟶ (158, 2853, 3722, 5988, 8270, 8541, 9835, 11310, 13110, 14451, 15023, 15339, 15453, 20082, 21077, 21455). Amoeba (B357/S1358, rule 150728) ⟶ (1911, 2836, 3535, 7974, 11374, 11804, 14164, 14847, 14991, 15696, 19335, 19352, 19900). Bugs (B3567/S15678, rule 195656) ⟶ (3316, 9023, 9224, 11141, 11382, 15016, 17788, 19364, 20642). Coagulations (B378/S235678, rule 256224) ⟶ (115, 1486, 3462, 3640, 11932, 12651, 13843, 14153, 14162, 16096, 17083). Day & Night (B3678/S34678, rule 258752) ⟶ (1549, 1738, 4325, 5729, 6138, 9414, 11771, 13260, 15426, 15513, 15590, 16487, 18861, 19951, 19979, 20551, 20880, 21149, 21449, 21481). Stains (B3678/S235678, rule 260320) ⟶ (115, 3640, 5900, 13695, 13965, 18511, 20317). Iceballs (B25678/S5678, rule 261136) ⟶ (195, 230, 231, 2430, 4252, 7684, 12388, 17294, 19493). Not all rules have gliders. There are no gliders known for Assimilation (B345/S4567, rule 44864), Coral (B3/S45678, rule 174656), Land Rush (B36/S234578, rule 170720), LongLife (B345/S5, rule 3392) or Maze (B3/S12345, rule 2792). Also, most rules do not have established names, with (B02/S4, rule 1552) being one example.
