In a
cellular automaton
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tesse ...
, an oscillator is a pattern that returns to its original state, in the same orientation and position, after a finite number of generations. Thus the evolution of such a pattern repeats itself indefinitely. Depending on context, the term may also include
spaceships as well.
The smallest number of generations it takes before the pattern returns to its initial condition is called the ''period'' of the oscillator. An oscillator with a period of 1 is usually called a
still life
A still life (plural: still lifes) is a work of art depicting mostly inanimate subject matter, typically commonplace objects which are either natural (food, flowers, dead animals, plants, rocks, shells, etc.) or man-made (drinking glasses, bo ...
, as such a pattern never changes. Sometimes, still lifes are not taken to be oscillators. Another common stipulation is that an oscillator must be finite.
Examples
In
Conway's Game of Life
The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined by its initial state, requiring no furthe ...
, finite oscillators are known to exist for all periods except 19 and 41. Additionally, until July 2022, the only known examples for period 34 were considered trivial because they consisted of essentially separate components that oscillate at smaller periods. For instance, one can create a period 34 oscillator by placing period 2 and period 17 oscillators so that they do not interact. An oscillator is considered non-trivial if it contains at least one cell that oscillates at the necessary period.
Image:2-3 O1.gif, blinker, period 2
image:JdlV osc 3.169.gif, star, period 3
image:JdlV osc 3.100.gif, cross, period 3
image:JdlV osc 3.90.gif, French kiss, period 3
image:JdlV osc 3.144.gif, clock 2, period 4
image:JdlV osc 3.144bis.gif, pinwheel, period 4
image:JdlV osc 5.64.gif, octagon
In geometry, an octagon (from the Greek ὀκτάγωνον ''oktágōnon'', "eight angles") is an eight-sided polygon or 8-gon.
A '' regular octagon'' has Schläfli symbol and can also be constructed as a quasiregular truncated square, t, w ...
, period 5
image:JdlV osc 5.56.gif, fumarole, period 5
image:JdlV osc 5.156.gif, pentoad, period 5
image:oscilador8periodos.gif, Kok's galaxy, period 8
image:JdlV osc 15.144.gif, pentadecathlon, period 15
External links
List of notable known oscillatorsat the LifeWiki
A collection of oscillators in the Game of Life(zip file)
{{Conway's Game of Life
Cellular automaton patterns