"Life without Death" ( Eng. Life without Death ) - a cellular automaton , a modification of the game "Life" . It was first described in 1987 by and , who gave it the name " Inkspots " [1] - since many configurations of the machine behave like a spreading ink stain. Also known under the name "Flakes" ( English Flakes ) [2] .
It is described by rule B3 / S0123456789: as in the game “Life”, a cell is born ( b irth) if in the vicinity of Moore it has exactly 3 living neighbors; but, unlike the game "Life", the cell survives ( s urvival) with any number of living neighbors.
Thus, any still life from the game “Life” is a still life in “Life without Death” (but not vice versa); however, due to the absence of cell death, there are no oscillators , spaceships , steam locomotives , rifles , etc. in Life Without Death.
Any still life from HighLife , Day and Night, and other modifications of the Life game with the rule for the birth and survival of cells of type B (...) 3 (...) / S (...) is also a still life in Life without death. "
Stairs and parasitic sprouts
In many evolutions of the automaton, ladders appear [3] : periodic patterns that can grow in a straight line unlimitedly - unless another object is in the way of their growth or overtakes them, growing at a higher speed. Most often, with a random initial configuration, the stairs shown in the examples below are born with a growth rate of c / 3; for every 12 generations, they move 4 cells forward.
Objects similar to stairs, parasitic shoots ( English parasitic shoots ) [3] , grow similarly, but not along an empty field, but along already grown stairs or other germs. The most common parasitic germ is at a rate of 2 c / 3.
Three stairs. The upper and lower stop, having encountered a simple still life from one living cell; the middle staircase, having met a stable object of four living cells, turns - and stops, colliding with the bottom.
(Only every 4th generation is shown.)Fast parasitic sprout on a slower staircase. When a sprout overtakes a ladder, a chaotic “explosion” occurs, ejecting two parasitic sprouts in the opposite direction.
(Only every 4th generation is shown.)
Using ladders, you can emulate logic gates and calculate Boolean functions [4] . The constants 1 and 0 in this case are represented by the presence or absence of a ladder in a certain position.
Notes
- ↑ Tommaso Toffoli, Norman Margolus. Cellular Automata Machines: A New Environment for Modeling. - MIT Press, 1987. - pp. 6-7.
- ↑ MCell lexicon of Cellular Automata rules .
- ↑ 1 2 Janko Gravner, David Griffeath. Cellular Automaton Growth on Z 2 : Theorems, Examples, and Problems / Advances in Applied Mathematics, 21 (1998). - pp. 241-304.
- ↑ David Griffeath, Cristopher Moore. Life without Death is P-complete / Complex Systems, 10 (1996). - pp. 437-447.
Links
- Life without Death in the LifeWiki Encyclopedia
- David Eppstein Faster ladders in Life without Death (2009)
- A Way-Cool CyberFlake on Primordial Soup Kitchen (1995)