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SUMMARY:Dynamics and computability in Game of Life
DTSTART:20230914T120000Z
DTEND:20230914T130000Z
DTSTAMP:20241006T202600Z
UID:indico-event-10343@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ilkka Törmä (University of Turku)\n\nThe Game of L
ife is a cellular automaton designed by John Conway in 1969. It consists o
f an infinite two-dimensional grid of cells\, each of which can be either
"alive" or "dead". The grid evolves in discrete time steps. If exactly 3 o
f the 8 neighbors of a dead cell are alive\, the cell becomes alive\; and
a live cell stays alive if it has 2 or 3 live neighbors. Despite the simpl
icity of the rule\, Game of Life has very complex dynamics and is notoriou
sly difficult to analyze.We present new proof techniques for studying the
long- and short-term dynamics of Game of Life (and other cellular automata
). Using them\, we show that: Game of Life does not reach its limit set in
a finite number of steps\; its dynamics on the limit set is not transitiv
e\; it is decidable whether a finite-population configuration has a predec
essor\; it is undecidable whether a totally periodic configuration has a p
redecessor\; there exists a finite-population configuration that has a pre
decessor\, but no finite-population predecessor\; and various other result
s.\n\nhttps://indico.math.cnrs.fr/event/10343/
LOCATION:Salle F. Pellos (1R2-207) (IMT)
URL:https://indico.math.cnrs.fr/event/10343/
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