Day 8
26 March 1998
Cellular Automata

Summary of this Day's Class
We finished our discussions on hierarchical organization. We talked about John Conway's Game of Life. A computer program was set up see the results of iterating various initial conditions. We saw that stable patterns, periodic patterns and regions of lots of activity were possible. We then tried modifying the rules to see what would happen to the possible patterns, and found that it is impossible to predict what will happen without trying it.

The relationship between cellular automata, and other topics relevant to complex systems were explored. We briefly discussed Bak, Chen and Creutz's paper on self-organized criticality in the Game of Life. The homework is designed to allow the student to investigate the meaning, importance, and relevance of the concepts of emergence and emergent properties, the idea that simple iterated rules can produce complex behavior, Howard Pattee's idea of the importance of extraordinary boundary conditions and the idea of a machine, John Holland's idea of building blocks, and the importance and usefulness of various levels of description.

Homework Assignment 8 - Due 2 April 98
Last week we played with John Conway's Game of Life with some very basic initial states.
Now we are going to aim a little higher and change our focus.

Go to the web site by Alan Hensel:
http://www.mindspring.com/~alanh/life/
and use the JAVA script Life simulation to study the pattern called BREEDER.
To view this press the OPEN button and wait patiently for a window containing a list of patterns to open.
Click on the pattern called BREEDER and wait for it to come up.
(If you had been playing around with the game previously, you may need to press the CLEAR SCREEN button before opening the pattern)

I want you to study the pattern closely.
You may need to change the scale on the screen using the ZOOM button so that you can view most of the pattern. The pattern is huge so scrolling around may be necessary as well.

Running this pattern you will see that it breeds an infinite line of glider guns.
You will see that there are spaceships that put along leaving trails and gliders eating things and so on.
For your homework you should describe in detail how this breeder works.

While you are working on this I want you to keep in mind several important ideas central to the study of complex systems:

• The idea that simple rules iterated repeatedly can create complex results demonstrated and discussed so extensively by Douglas Hofstadter, Benoit Mandelbrot, and Richard Voss.
• The idea and meaning of emergent properties.
• Howard Pattee's insistence on the importance and independence of boundary conditions from basic laws.
• John Holland's ideas of building blocks.
• The idea of various levels of description.

here:

Reading Assignment 8 - Read the articles by 2 April 98
Have emailed comments by NOON Wednesday 1 April 98

Abraham, Ralph H. and Shaw, Christopher D. 1992. Basic concepts of dynamics, Chapter 1 in: Dynamics: The Geometry of Behavior, 2nd ed., Addison-Wesley, Redwood City CA, pp. 13-51.

Abraham, Ralph H. and Shaw, Christopher D. 1992. Classical applications, Chapter 2 in: Dynamics: The Geometry of Behavior, 2nd ed., Addison-Wesley, Redwood City CA, pp. 53-85.

Zeeman, E.C. 1976. Catastrophe theory, Scientific American, 4:65-83.

Zeeman, E.C. A catastrophe machine, Appendix in "Towards a Theoretical Biology Vol. 4", Ed. C.H. Waddington, International Union of Biological Sciences and Edinburgh University Press, Edinburgh, pp. 276-282.