Greedles, greedles, and more greedles!


Even more background information on the Game of Life

A short history of the Game of Life

Some reasons why the Game of Life is pretty neat

Books we found helpful in exploring the Game of Life

A short history of the Game of Life

cellular automaton: 'sel-ye-ler o-'ta-me-ten n [L cellularis automatos ] (1950) : a car equipped with a phone.

The Game of Life originates with the concept of a 'cellular automaton' and famous person John von Neumann. In the 1950's, von Neumann was interested in exploring the possibility of machines that could self-reproduce (hey, who hasn't been interested in that at one time or another?). To grapple with this issue, he needed to

"abstract from natural biological self-reproduction the logical form of the reproduction process, independent of its material realization in any particular physico-chemical form" (Casti, 211).

Yikes! - that seems like a tall order...

but not all that tall if you look closely. Basically, what was needed was a way to experiment with the 'essence' of reproduction, without having all the squishy stuff (blood, muscles, etc.) get in the way. This necessary abstraction was eventually accomplished through cellular automata - not to be confused with cellular laundromata, which failed miserably, largely because von N. kept losing socks in them.

So, what exactly is a 'cellular automaton'?

"The Game of Life is an example of a general class of processes known as 'cellular automata'. The Game of Life is said to be cellular because the same transformation rule is applied at each of the cell sites; it is like an automaton, or computer, in that it accepts data input in the form of the starting pattern of marked cells, it changes this data in accord with definite rules, and it gives you data output in the form of the new pattern of marked cells. A generalized cellular automaton can be thought of as a large array of independent, identically programmed computers, one per cell" (Rucker, 113-114).

Okay, okay - time to slow down a bit. There's a computer in each of the little boxes in our matrix?! ( YES! FEEL THE POWER OF SHOCKWAVE 6 - NOW WITH PARALLEL PROCESSING! ) Well, in a sense, there is - a very simple computer.

If you will recall, there was a section in the Game of Life's instructions that explained the rules a greedle followed when it counted its immediate neighbours and decided whether to live, die, or reproduce. Here's a somewhat more compact way of expressing these same rules (note that we will call the little boxes in the matrix 'cells' from now on):

(1). If a cell (whether empty or occupied) has exactly 2 neighbours, then it does not change in the next generation (in other words, it remains empty if it was empty before, or occupied if it was occupied before).

(2). If a cell (whether empty or occupied) has exactly 3 neighbours, then it will be occupied in the next generation (in other words, it will stay occupied if it was occupied already, or a new greedle will be born into the cell if it was previously empty).

(3). If a cell (whether empty or occupied) has any number of neighbours other than 2 or 3, then it will be empty in the next generation (in other words, it will stay empty if it was empty already, or the greedle in it will 'pass on to a better place' if the cell was previously occupied). (adapted from Casti (who, to our knowledge, has never used the word 'greedle' before), 169)

There - we've compressed the original 4 rules to 3, thanks to Dr. Casti. Now, if we conceive of:

- each cell as a tiny independent computer (with the 3 rules being the 'program' running on it),
- the number of neighbours around the cell as the data 'input' to the cell-computer, and
- the status of the cell in the next generation (occupied / unoccupied) as the 'output' of the cell-computer,

you'll be able to see how each cell can be viewed as a simple computer, processing input and generating output with every passing generation of the greedle colony. We will call this simple computer an automaton - and since each automaton lives in its own cell in the matrix, we have 'cellular automata'. Ta-da!

Although Von Neumann (the pappy of the serial computer, by the way - yes indeedy, he invented the computer that you get at the bottom of your box of Rice Krispers - what a marketing genius!) was responsible for the concept of cellular automata, it was famous person John Horton Conway who created the Game of Life out of it. The Game of Life is likely the most well-known and studied example of cellular automata, and with its metaphorical representations of 'birth', 'life', 'evolution', and 'death', can be quite a joy to play with.

That's enough for now. Class dismissed.

If you're interested, we can elaborate more on the Game of Life in future installments, including:

Excerpts from the paperback bestseller, "Horton Hears The Who", John Horton Conway's semi-autobiographical account of how the song 'My Generation' (which he heard constantly in his college dorm) inspired him to study evolution in the first place.

And the differences between a Von Neumann neighbourhood (where diagonal cells are not considered adjacent cells, so the maximum number of neighbours possible is 4), a Moore neighbourhood (which includes diagonals, so the maximum is eight neighbours), and Mr. Roger's Neighbourhood (where everyone is diagonal, and everyone wants to be your neighbour).)

Some reasons why the Game of Life is pretty neat:

(Sorry, no time to list reasons yet. We've been too busy playing with the game and coming up with cool patterns. But, if you'd like to submit some reasons - or some patterns - feel free.)

Books we found helpful in exploring the Game of Life:

Casti, J. L. (1992). "Reality Rules: Volume 1". (See also the companion volumes "Reality Rocks: Volume 2", "Reality Bites: Volume 3", and "The Return of The Bride of Reality Bites: Volume 4") New York, NY: John Wiley & Sons. (ISBN: 0-471-57021-4)

Dawkins, R. (1976). "The Selfish Gene". New York, NY: Oxford University Press. (ISBN: 0-19-217773-7)

Gardner, M. (1983). "Wheels, Life and Other Mathematical Amusements". San Francisco, CA: Freeman. (ISBN: 0-71-671-5899)

Kaplan, D., & Glass, L. (1995). "Understanding Nonlinear Dynamics". New York, NY: Springer-Verlag. (ISBN: 0-387-94440-0).

Kelly, K. (1994). "Out Of Control". New York, NY: Addison( aim is true)-Wesley. (ISBN: 0-201-48340-8)

Roetzheim, W. H. (1994). "Enter The Complexity Lab". Indianapolis, IN: Sams Publishing (ISBN: 0-672-30395-7)

Rucker, R. (1987). "Mind Tools". Boston, MA: Houghton Mifflin Co. (ISBN: 0-395-38315-3)

Thro, E. (1993). "Artificial Life Explorer's Kit". Indianapolis, IN: Sams Publishing (ISBN: 0-672-30301-9)

(see also the M.I.T. journal, Artificial Life (ISSN: 1064-5462).)

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