In 1970 and 1971 I read a pair of articles in Scientific American on Cellular Automata and John Horton Conway's game of Life. I immediately became fascinated with the subject and spent many hours working through the examples on graph paper (a very tedious exercise) and then, writing computer programs which performed this work automatically.

For those of you who haven't seen it before, Life works like this. Imagine a large (in theory, infinitely large) flat surface laid out in a regular two-dimensional rectilinear grid. Each space on this surface is called a cell and each cell has eight neighbours (including those that touch only on the corners). A cell may be either alive or dead, and the rules are as follows:

• a live cell with 0 or 1 live neighbours dies of loneliness
• a live cell with 2 or 3 live neighbours survives
• a live cell with 4 or more live neighbours dies of overcrowding
• a dead cell with exactly 3 live neighbours "gives birth"

The rules are applied to every cell at once, and then the same rules are applied again in a succession of "generations".

The rules were chosen by Conway after much experimentation because they result in an interesting balance - some combinations of cells remain stable, some enter repeating sequences, cycling through the same patterns every two or more generations, and some create structures of amazing complexity.

For example, four live cells in a square configuration are stable, because each has three live neighbours.

Three live cells in a row form a repeating pattern because on each generation the cells at each end die, but new cells are born either side of the center cell, reproducing the three-in-a-row pattern at right angles to the original.

And a pattern of five cells known as the r-pentamino produces an explosion of activity that doesn't quieten down until over 1000 generations have passed. This is the pattern that was used in the example at the start of this page, and among the generated patterns can be seen a number of "gliders", groups of five cells which re-create themselves at a slight offset, thus appearing to "walk" across the grid.

(The illustration at the top of this page is an "applet". For more about applets see here.)

Life is an example of a class of conceptual frameworks called Cellular Automata (CA). Life is a two-dimensional Cellular Automaton, but there are also one-dimensional Cellular Automata and in theory a CA could have any number of dimensions. Life has two states - alive and dead - but there are examples of Cellular Automata with far larger numbers of states and far more complex rules governing the transitions between those states.

Stephen Wolfram is a genius. That is not a word I use lightly, since I have known a number of people with very high IQs, but I think in his case the term is clearly justified. He received his Ph.D. in theoretical physics at the age of 20, and later founded Wolfram Research, Inc. where he produced the system Mathematica which is now one of the world's leading systems for mathematical and scientific computing.

I don't know whether Wolfram read the same Scientific American articles that I did, but at some stage he obviously became very interested in Cellular Automata. But while I casually dabbled in the subject over a period of years, Wolfram immersed himself in CA, devoting many years of his life to very intensive research into the field.

The result of all this effort is a self-published book called A New Kind Of Science. In it, Wolfram sets out his research into Cellular Automata in great detail, and then goes on to draw some very controversial conclusions from that research. To say that the book has had a mixed reception would be a considerable understatement.

One reason for criticism is the name of the book. Many people have questioned whether the word "New" in the title is justified, since Conway and John von Neumann, among others, were working in this field decades ago. Wolfram might claim that his inferences take Cellular Automata into a whole new area - postulating that CA may underly the whole of theoretical physics - but to say that this constitutes a new kind of science is a bit of a stretch. A new application of existing science, perhaps.

The academic community have also got their knickers in a twist over Wolfram's chosen method of publication. They would have liked him to submit a paper to one of the respected publications, such as the journal Nature, which would then have kicked off a standard process of peer review. Wolfram seems to have preferred the review of the marketplace.

And something which seems to have got everyone's backs up, including mine, is Wolfram's use of the first person singular throughout the book. Perhaps a quotation from the very first page will illustrate:

It has taken me the better part of twenty years to build the intellectual structure that is needed, but I have been amazed by its results. For what I have found is that with the new kind of science I have developed it suddenly becomes possible to make progress on a remarkable range of fundamental issues that have never successfully been addressed by any of the existing sciences before.

Clearly, Wolfram is a man not over-burdened by modesty.