Game Of Life

The GameOfLife is a very simple CellularAutomaton invented by JohnHortonConway and popularized by the writings of MartinGardner in ScientificAmerican (e.g., Scientific American 223 (October 1970): 120-123). GOL is capable of universal computation and of self-reproduction, but is vastly simpler than the first CellularAutomaton capable of self-reproduction, discovered in the 1940s by JohnVonNeumann.

A quest was launched to find programs (configurations) with interesting properties. For many it was a first taste of non-VonNeumannArchitecture.

http://www.cpdee.ufmg.br/~seixas/PaginaATR/Download/DownloadFiles/MathematicalGames.pdf
http://www.math.com/students/wonders/life/life.html -- introduction and explanation
http://www.radicaleye.com/lifepage/ -- catalog of discoveries with a Java applet to run them
http://www.ibiblio.org/lifepatterns/ -- another collection

What fascinates me is that the patterns that do something useful are often very decorative. They look at first sight as if they may contain a lot of AlexandrianCenters. Does anyone else share this impression? -- KeithBraithwaite

CocoaWorlds offer modern kids another alternative.

The GameOfLife is a CellularAutomaton, a classic piece of theoretical computer science, the foundation of JohnVonNeumann's self-reproducing system (so CellularAutomata are not in fact non-VonNeumannArchitecture!), and a good example of ArtificialLife. -- BillTozier

It is possible to build Life modules that act as logical AND, OR and NOT gates, therefore a TuringMachine, and therefore any computable model (including self-awareness if self-awareness is computable). (True, but with all the other interesting capabilities of the game, is seems a shame to "reduce" it a mere Turing computing engine. Seems more more interesting to discover NonTuringComputing with it.)

Oh, I beg to differ! Isn't this the inverse of "reducing" it? It seems to me that this demonstration proves that it is larger, and therefore more interesting.

The solution to this paradox is that ReductionIsGood?. It sounds like a negative term, but it isn't. For me, reduction is almost synonymous with understanding.

This is also a graphic demonstration that emergent behavior at one abstraction level can be used to construct deterministic systems at another. This puts to bed, in my view, the logical fallacy that underlies many arguments against artificial life and artificial consciousness. The observed presence of "order" at one abstraction level (such as when looking at the elements of a computing engine built from Life) does not imply intentional design at lower abstraction level (such as the rules of the environment in which those elements operate).

-- TomStambaugh

In late 2000, a TuringMachine has been demonstrated in a 1714 x 1647 GameOfLife pattern implementing a 3-state 3-symbol machine which takes 11040 generations for a single cycle. Pictures and explanations at:

The author says: "The design for this Turing Machine is extendible by expanding the size of the Finite State Machine part and storing different numbers in the memory cells. The maximum size is 16 states and 8 symbols. This is sufficient for a Universal Turing Machine."

That thing looks amazingly like models of DNA transcription!!!

The GameOfLife was one of the seeds of StephenWolfram's search. He states everything can be explained through simple self-replicating rules. He wrote a gigantic book about it, A NewKindOfScience. Now published online: http://www.wolframscience.com/.

There is a ForthLanguage implementation of the GameOfLife on ForthBlocks.

In a different sense: RealLife GameOfLife

In the context of your own life, the GameOfLife has to be played on a field where LifeIsaBigMessyGraph.

In RealLife, the GameOfLife is likened to be engaged in "Concurrent Attention-Seeking Games": GameOfChess, WarGames, TelephoneGame, PokerGame, HangmanGame, GameOfPong, etc all in time limited fashion. The involvement alone stops people from exploring MeaningOfLife in a meaningful manner.

CategoryMath