In my opinion, every philosophy student should be held responsible for an intimate acquaintance with the Game of Life. It should be considered an essential tool in every thought-experimenter’s kit, a prodigiously versatile generator of philosophically important examples and thought experiments of admirable clarity and vividness.
Daniel Dennett, Real Patterns
Life is played on a two-dimensional grid, such as a checkerboard or a computer screen; it is not a game one plays to win; if it is a game at all, it is solitaire. The grid divides space into square cells, and each cell is either ON or OFF at each moment. Each cell has eight neighbors: the four adjacent cells north, south, east, and west, and the four diagonals: northeast, southeast, southwest, and northwest.
Time in the Life world is also discrete, not continuous; it advances in ticks, and the state of the world changes between each tick according to the following rule:
Each cell, in order to determine what to do in the next instant, counts how many of its eight neighbors is ON at the present instant. If the answer is exactly two, the cell stays in its present state (ON or OFF) in the next instant. If the answer is exactly three, the cell is ON in the next instant whatever its current state. Under all other conditions the cell is OFF.
Ibid.
(I like Daniel Dennett’s introduction to the Game of Life, and I want to give him credit for taking this game seriously as a philosopher back in the nineties, but I will use the terms ‘live’ and ‘dead’ where he uses ‘ON’ and ‘OFF’.)
These simple rules allow countless different patterns of live cells to emerge in the Game of Life, but despite the potential diversity and complexity of these forms, they all fall into four categories: Static, Stable, Mobile, and Dynamic.
Static forms are the simplest. They do not change from one tick to the next. In order for this to be the case, they have to meet two conditions. First, every live cell in the pattern must have two or three live neighbors (else it would die at the next tick); second, no dead cell adjacent to the pattern can have exactly three live neighbors (else it would come alive at the next tick).
The next simplest patterns are the Stable forms, which begin in one state and cycle through a number of different states before returning to their original state to repeat the cycle. Many of these forms oscillate between two states, but there is theoretically no limit to the length of the cycle. The number of states in this cycle is called the form’s period, and you can think of a Static form as like a Stable form with a period of one.
Mobile forms also feature a repeating cycle of states, but with a twist: when a Mobile form gets back to its original state, it’s in a different position on the board! The most famous mobile form is the Glider, which has a period of four and moves diagonally, at a rate of one square every four ticks, meaning that every four ticks, its initial configuration reappears, one square to the NW/NE/SW/SE. The Lightweight Spaceship, on the other hand, also has a period of four, but it moves rookwise (N/S/E/W) at a rate of one square every two ticks, meaning that it has advanced two squares by the time its initial configuration comes back around. Because information can propagate across the grid at a maximum speed of one square per tick, this rate is conventionally called c, after the physical constant for the speed of light. Thus, the Glider has a speed of c/4, while the LWSS moves twice as fast, at c/2. If it helps you, you can also think of Stable forms as like Mobile forms with a speed of zero.
The vast majority of patterns that can be created in the Game of Life fall under the last category of Dynamic forms. This is sort of a grab-bag category for anything that doesn’t behave in a way that’s easy to characterize, but within this category is where the magic happens. Dynamic forms grow and change; they multiply and divide and proliferate across the board. Forms like the r-pentomino seem to explode and keep exploding, throwing off Static, Stable, and even Mobile forms as shrapnel, until the Dynamic part peters out altogether, leaving in its wake a “decay signature” of these simpler forms.
The point of playing the Game of Life is to create patterns that evolve in interesting ways, whatever sort of theoretical or aesthetic properties you find interesting. You can use it to simulate computational machines, demonstrate fundamental principles of emergent complexity, and create strikingly beautiful symmetries. The possibilities are truly infinite.
There are already a few different versions of this game that you can play online, but I’d like to think that mine has the greatest “fun factor”. It’s a sandbox, made for you to really play around and get your hands dirty, or to provide objects of contemplation like a digital Zen garden.
Click a cell on the board to flip it from live to dead or vice-versa. You can also select a pattern from the menu below the grid and drop it anywhere on the board with a click. Shift-click keeps the pattern on your cursor so you can drop multiple copies of the same pattern.
Hit the space bar to start and stop the game. Right and left arrow keys advance the game forward or back by one tick, while up and down adjust the speed.
Create a pattern by clicking on the board, or select a pattern from the menu to get started.
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