The creator of the Game of Life is dead. John Conway is another victim of the coronavirus

John Horton Conway, an English mathematician known for his achievements in many fields of mathematics, died on April 11 at the age of 82. The cause of death was COVID-19 infection.

Conway worked during his long career on game theory, topology, mathematical analysis, algorithmics, set theory and number theory. He was the creator of the concept and definition of surreal numbers. However, he was best known for his Game of Life - a simple cellular automaton that meets the definition of a Turing machine.

The death of this great mathematician is a sad but good opportunity to tell about the great and inspiring game scientists and developers, invented by Conway.

A game of life

Imagine a plane with an infinite surface divided into squares. Each box can be either filled (live) or empty (dead). The cell has a maximum of eight neighbors, bordering it sideways or corner of the grille.

Time on this plane flows discreetly, step by step, i.e. just like in turn-based games. There are no intermediate states. The state of the plane in each subsequent step depends entirely on the state in the previous step.

In the first step, we arrange some pattern from living cells on the plane. The game of life begins. Conway has created three simple but ingenious rules for his game:

  • a living cell with two or three neighbors will still be alive in the next generation
  • a living cell that has one or zero neighbors dies of loneliness
  • a living cell that has four or more neighbors is dying of congestion
  • an empty cell with exactly three living neighbors becomes alive.

These simple rules are enough for the situation on the board to change dramatically from generation to generation, becoming hard to predict after just a few iterations. It has actually been proven that without running the machine, it is not possible to predict the state of the board using a different algorithm. These types of games (called cellular automata) can be used for many purposes - including simulating real phenomena, e.g. the spread of epidemics.

Gospers glider gun

When we play a game of life we ​​notice that chaos often leads to order.

Even randomly placed cells on the board often turn into a series of patterns - stable, cyclic or dying. Fans of this game for many years since its creation are still looking for typical so-called oscillators, i.e. cyclic patterns. Ships that can "move" on a plane in a specific direction and the so-called department - colonies of cells generating "cartridges", i.e. mini-ships. Interesting for game lovers are also the so-called gardens of Eden. These are combinations of cells that cannot have the previous generation because they could not arise from any other combination based on given rules.

An example of a stable structure that does not change over time:

An example of a simple oscillator

Game of life blinker

And here is the so-called Glider: a spaceship moving on a plane

Game of life animated glider

To play the game on your own (or any other cellular machine based on a similar idea), we can use the Golly app . This small open-source program is available on every operating system, including mobile devices.

Main image Thane Plambeck from Palo Alto, California - Flickr , CC BY 2.0 , Link

The creator of the Game of Life is dead. John Conway is another victim of the coronavirus


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