Oct 31 2010

The Game of Life

I

recently put a picture of myself (circa mid-70′s) on my Facebook page. It generated quite a few comments, but by far the most interesting came from Kristin, a long-time web friend, who asked “what words of wisdom could I give to that young man in the photo?” I replied that my advice would be –that if he were around long enough– he’ll probably have to live with all his choices, but not necessarily all his circumstances.

A decidedly deterministic take on things I’ll admit, but still, a rather useful heuristic that apparently does find its place in more life processes then you’d think.

The Game of Life, or simply Life, was invented in the early 1970′s by the mathematician John Horton Conway. Life is a zero-player game, meaning that its evolution is determined by the initial state of the cells and thus requiring no further input. Executed on a grid of squares (cells), each in one of a finite number of states (much like the ancient game of Go) you interact with Life solely by creating an initial configuration and then simply observing how it evolves —typically through some sort of computer algorithm. Like real life, Life evolves through iteration, and iteration requires the dimension of time.

In the Life grid of squares a “cell” can be live or dead. Putting a marker on its square shows a “live cell.” A “dead cell” is simply an empty square. Each cell in the grid has a neighborhood consisting of the eight cells in every direction including diagonals. Life’s evolution is determined by its initial state, requiring no further input from humans. One interacts with Life by creating an initial configuration, turning it on, and observing how it evolves.

Life has some very simple rules, which are repeatedly run with each iteration of the game:

  • A empty cell with exactly three live neighbors gives birth to a new cell.
  • A live cell with two or three live neighbors survives and stays alive.
  • In all other cases a cell dies or remains dead (from either “overcrowding” or “loneliness”).
  • The number of live neighbors is always based on the cells before the rule was applied. In other words, we must first find all of the cells that change before changing any of them.


Rules for Conway's 'Life'


Despite its simplicity, Life achieves an impressive diversity of behavior, fluctuating between apparent randomness and order. One of the most interesting features of Life is the frequent occurrence of “gliders” (arrangements of cells that essentially move themselves across the grid) and other high order-clusters of organization.

Life is just one example of a cellular automaton, any system in which rules are applied to cells and their neighbors in a regular grid. It is one of the simplest cellular automata to have been studied, but many others have also been invented, often to simulate systems in the real world. Life is the study of how elaborate patterns and behaviors can emerge from very simple rules. It helps us understand, for example, how the petals on a rose or the stripes on a zebra can arise from a tissue of living cells growing together. From a theoretical point of view, Life is interesting because it dynamically has the power of computation: Conway was able to show that Life in certain circumstances could model a “universal Turing machine,” essentially a very basic computer.

Possibly because it was viewed as a largely recreational topic, little follow-up work was done outside of investigating the particularities of Life and a few related rules.

Life is a intricate web of many simple components acting in complex ways.

Conway’s Life is one of the simplest examples of what is sometimes called emergent complexity or self-organizing systems.

The complexity of an object or system is a relative property. A fundamental feature of complex systems is that they consist of many (or at least several) integral parts that are connected via their interactions. Their components are both distinct and connected, both autonomous and to some degree mutually dependent. It is more or less universally accepted is that complexity is situated in the time-space between order and disorder.

Fifty years ago, if a group of scientists were asked to define the key to life, the great majority would point to metabolism; how we obtain energy from food. However, adding all the required molecular components and stirring it up will not produce an organism. A more modern view of molecular biology is concerned with organization in time and space. How do the molecules of life arrange themselves throughout the cell’s compartments, how do they move around, and communicate so as to synchronize their actions? We can ask this question because we can now inspect the working cell at a molecular level and take snapshots of its molecules doing their business. And it is a community of daunting complexity.

There’s no sense in being precise when you don’t even know what you’re talking about.

—John von Neumann

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