THIRD LECTURE: Jan 17, 2007

Embryology Biology 441 Spring 2007 Albert Harris


The concept of rule-generated patterns (including rule-generated structures)

Spatial patterns can be created by cumulative effects of interactions between parts. For example, even long-range effects of cells on each other can produce long-range geometric patterns.

This is one of the most important concepts to get used to in embryology and developmental biology. For many people (scientists as well as students) this isn't part of their "common sense", and is something they need to learn. The only way to learn it is to see examples.

To help you learn this concept (that the cumulative effect of close-range effects can be long-range patterns) we provide a simple computer program was called "CellAutomata". This program was written in JAVA by a former student in this course named Andy Wheeler, who has graduated and gone on to medical school. This program runs on PCs and also Macs, and is posted under "Courses" on my faculty web site (link). If you play with this program for a few hours, especially while listening to Mozart, the effect will raise your IQ by eleven points. Maybe more!



Anyway, it will definitely give your intuition a head-start in thinking about how embryos generate anatomical patterns. It moves you beyond the "genes are blueprints for anatomy" over-simplification. Of course, cell automata are also simplifications, but some serious science has been done with them. They were first developed by two of the best mathematicians at Los Alamos in the Manhattan Project, and hundreds of books and research papers have been written about them. The best recent book on the subject is "A Whole New Kind of Science" by Steven Wolfram, which I highly recommend in case you get addicted. His favorite word is "vast", and his ideas are more than 50% vast. Since Newton, Physics has been based on matching phenomena to differential equations. From now on, we may need to substitute cellular automata for equations. Mathematicians are outraged by this prospect. Biologists should welcome it.

Many other people besides me have have cellular automata programs posted on their web sites. Our program is meant to be:

    * Helpful to people learning embryology.
    * As easy as possible to use.
    * Somewhat fun.
    * NOT a simulation of any particular biological or other phenomenon.

(Until you get the 11-point IQ-boost, you probably won't see the relevance! Afterward, you will get the point. But to explain it to other people, you will need to show them the cellular automata program!)

Incidentally, if you ever do write computer simulations of specific spatial phenomena, don't be surprised that the underlying structure of your program will turn out to be some kind of cellular automaton. I have written more complex versions (on Macs) in which the units * move around, * pull and push on each other, * react differently to near versus far neighbors, &c.

Furthermore, for anyone who doubts the reality of "emergent properties", they should notice that (on a PC) if you try to start the pattern with a straight line more than a few squares long, this will cause the program to crash. A five-$ reward to anyone who can invent a reasonable explanation!


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