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Warp Life 1.0 User Guide

Our personal take on the Cellular Automaton
known as John Conway's Game of Life.

Warp Life is a simple graphical game that implements Conway's Game of Life. It was invented by Computer Scientist John Conway in the early 1970s.

Conway's Life is a Cellular Automaton. Cellular Automata operate on N-Dimensional grids that store the automaton's state. A set of rules controls the state of each grid cell as the automaton propagates from generation to generation.

Conway's Life uses a 2-Dimensional grid. Its rules give rise to interesting patterns, many of which move or oscillate or exhibit unusual behavior.

Some Cellular Automata solve useful computational problems. If you can solve a problem with a Cellular Automaton, it is easy to model in software so you can get the design right, then easy and inexpensive to implement directly in hardware so you can build a parallel processing supercomputer!

The Rules of Conway's Game of Life

The grid is a 2-Dimensional array of cells. Each cell is either Alive or Dead. Living cells are black while the blue cells are Dead.

The fate of each cell in the next generation depends on its current state as well as how many living neighbors it has. Neighbors are counted both orthogonally and diagonally for a maximum of eight living neighbors.

If a cell has zero or one neighbor, it dies of loneliness.

If a cell has four or more neighbors, it dies of overpopulation.

If a cell has two neighbors, it stays the same. If it was Dead, it stays Dead. If it was Alive, it survives.

If it has three neighbors, it will be Alive in the next generation. If it was Dead, a new cell will be born.

A Simple Example

There are many well-known patterns in Conway's Life. We refer to them as "Animals". One such Animal is known as the Blinker or Traffic Light. It consists of a row of three living cells:

Vertical Blinker

Vertical Blinker

Let's count up the non-zero neighbors:

Blinker Neighbor Count

Blinker Neighbor Count

You can see that the cells at top and bottom will die while the cell in the middle survives. New cells are born to either side of the middle one, yielding a horizontal row of three cells:

Horizontal Blinker

Horizontal Blinker

Conway's Life'sules are symmetric with respect to ninety degree rotations as well as horizontal and vertical reflections, yielding eight-way symmetry. Thus the next generation after this one will restore the vertical stack of three cells. Therefore the Blinker is an oscillating pattern with a period of two.

Animals

There are many oscillators with periods of just one. These are known as "Still Lifes" because they are eternally unchanging.

Still Life

A Still Life

When you first play the game, see if you can come up with an oscillating Animal that moves to a new position in the grid at the end of a cycle. Such moving animals are known as "Space Ships". The Glider is the simplest such Space Ship. There are even Animals called Glider Guns that repeatidly eject new Gliders!

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