The game of life encyclopedia

  • BokkaB
    12th January Member 1 Permalink

    Hello,people!Do you know something about game of life?If not,I will tell you something.

    What is game of life?

    Game of life is a matematical simulation created by John Corton Conway and published in 1970. (it is 50th birthday of it this year!)

    How it works?

    Game of life universe is a plane with cells. Every cell has 8 neighbours and this is called Moore neighborhood (there also exists other neighborhoods,such as von Neumann neighborhood where there are no diagonal neighbours,hexagonal,circular....).

    The universe changes trough steps,that are called generations. If a cell has exactly 2 or 3 neighbours,it remains the same in the next generation,otherwise it dies(dissapears).

    When a dead cell has exactly 3 neighbours,it is born. This is systematically written as B3/S23,where B is born,and S is survive.


    Still lifes

    Patterns that never change are called still lifes. The most common one is a block,that looks like square. Other notable ones are beehive,loaf,boat,ship and so on. They are often born in a constellations of four. This is called pseudo still life since 

    parts can be removed and pattern will remain stable. However,there exists a still lifes that have more than one part(systematically called ,,island"),but they cannot be removed if we want for the pattern to remain stable. Examples are aircraft carrier and table on table. I will write about still life called eater 1 in Spaceships.


    Oscillators are patterns that periodically change. The most common one is a blinker,that looks like one cell thick row of 3 cells and that can be born in constellation of four ones called traffic light. Other notable ones are toad,beacon,suprisingly big pulsar and pentadecathlon(it has a period of 15). They often produce dying parts that are called sparks. An oscillator where every cell dies every generation,but pattern never dies is called phoenix.


    Patterns that periodically change over time,but also move are called spaceships. The most common one is a glider. Other,much less common ones are lightweight spaceship,middleweight spaceship and heavyweight spaceships. They can be abbreviated as LWSS,MWSS and HWSS. All other naturally occuring ones are combinations of three previous ones. However,there are many constructed spaceships. 

    Spaceships have their speed. It is compared with lightspeed (one cell per generation). It is written as c/n,where n can be any number of generations. Glider travels at c/4, LWSS,MWSS and HWSS at c/2. Most spaceships travel orthogonally or diagonally,but there also have been constructed oblique spaceships that travel in some other direction. Glider travels diagonally and LWSS,MWSS and HWSS orthogonally. 

    There exists patterns,mostly still lifes,that can ,,eat"them. More preciously,they can destroy spaceships and remain the same. The most notable one is eater 1. They also may eat still lifes,methuselahs and other patterns,for an example block can eat a beehive(and some other patterns).

    They can be produced by stationary patterns called guns or by movable patterns called rakes. If movable pattern produces objects other than spaceships (or small amount of them and other objects),it is called puffer. If pattern produces a second pattern that produces third pattern,it is called breeder.


    Methuselahs are small patterns,but that need very much time to stabilize. The best known ones are R - pentomino (5 cells,but 1103 generations to stabilize),Herschel,century and so on.

    There exists many more pattern types,but they are not for game of life beginners.

    Why is game of life important?

    Game of life is Turing - complete,means that it can simulate any machine,mostly using gliders.

    Other rules and algorithms

    It is possible to make many other rules by changing some parameters. Some notable ones;

    B36/S23:HighLife,extremly similar but with a replicator (pattern that produces infinite copies of itself. Recently have been constructed similar patterns in game of life.)

    B38/S23:Pedestrian Life,similar to game of life but with natural oblique spaceships and interesting puffers and an odd gun.

    B2/S:Seeds,extremly exploding rule where cells never survive.

    B3678/B34678:Day and Night,rule in that live cells in sea of dead cells behave the same as dead cells in the sea of live cells.

    B35678/S5678:Diamoeba,rule with diamonds with unpredictable behaviour.

    B345/S5:LongLife,rule with very high period oscillators and where spaceships are impossible.

    There also exists  many other algorithms:

    Generations,where cells may stay some time before dying and change color during this time.

    Notable rules:

    12/34/3(in this algorithm,first part is for survive,second for born and third to stay before dying):Frogs.


    34578/257/16:Spaceships and diamonds,rule devised by me.

    Larger than Life,where extended neighborhood can exist.

    Notable rules:


    LifeHistory,where can be seen all cells that were alive at least once. In ,,Golly",it is only avaiable for game of life.

    Non - totalistic rules,where cells are born and survive only if cells form a specific shape. Table can be found in ,,Golly" or at LifeWiki or Wikipedia.

    Notable rules:



    B2-aS12:Just Friends.

    Margolus neighborhood,where cells are joined in squares and change together.

    Notable rules are Critters and Tron,where cells only change if blocks have only one color.

    von Neumann rules,complex rules with replicating and computing behaviour.

    Additional rules:WireWorld, ant by Langton....

    Message for moderators

    Please do not lock this. I predict that game of life will be very important in the future,so I want to make an impact.


    Best program:Golly

    Have a good day!



    Edited 7 times by BokkaB. Last: 13th January
  • Palpatine333
    12th January Member 0 Permalink

    wow. i learned something, but idk what. this is so complex. but i learned something

  • BokkaB
    14th January Member 0 Permalink


  • BokkaB
    18th January Member 0 Permalink


  • Mrprocom
    18th January Moderator 0 Permalink
    @BokkaB (View Post)
    If you have nothing new to say, please don't bump the thread. We consider this spam (Rule S2) and it will probably get you in trouble if you do it again.
  • BokkaB
    18th January Member 0 Permalink

    I only do it to back it to the front page. I will stop.

    Have a good day!