# 2D CA Glider Database

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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.

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Contributed by: Ed Pegg Jr (June 2017)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The data in [1] was modified in the following ways:

2. All gliders were reoriented to have displacement not going down or to the left.

3. The "smallest" 0-background 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:

Knight-gliders. 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.

References

[1] D. Eppstein. "glider.db." (Jun 9, 2017) fano.ics.uci.edu/glider.db.

[2] D. Eppstein. "Which 'Life'-Like Systems Have Gliders?" (Jun 9, 2017) www.ics.uci.edu/~eppstein/ca.

[3] Wikipedia. "Glider (Conway's Life)." (Jun 9, 2016) en.wikipedia.org/wiki/Glider_(Conway's_Life).

## Permanent Citation