Last Friday I attended the Spring MATYCONN meeting with my infamous colleague Sue. I was treated to a really excellent tour of the Mandelbrot set by BU prof Robert Devaney. Where most presentations of fractals seem to die in the pictoral realm, Devaney gave the necessary background to appreciate the pictures and inner patterns of the set. He also had some cool visualizations. He's got some of them posted on his homepage.
pic by Fermion
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The Mandlebrot set is something that hit me like John Conway's "Game of Life." Both lend themselves to a computer program. The routines that drive them are very simple. What they produce is anything but.
I wrote a program in BASIC that sent a bit stream that my "Graftrax" Epson dot matrix printer could handle.
A fellow I was conversing with took my program and used a few of its ideas to build a program in his favorite language, Pascal. His program was a masterpiece and was *way* cooler than mine.
I thought readers would enjoy one of my favorite images from his program. Here it is.
mandelplotPS - I could provide links to source code, newsletter articles, information on emulators that allow all this code that was written for processors and printers that were big in the 1980s to still run, etc. But I'll stick with letting you imagine how I "wasted" my time then.
How do you "waste" your time?
Are you comparing the Mandlebrot set to the board game Game of Life, the one where you spin the wheel and get different professions, etc.?
No. I probably should have said "Conway's Life." This is something that was written up in October's 1970 issue of Scientific American by Martin Gardner. You might not have heard of it.
Conway's Life and the Mandelbrot set are related only in that both are based on a simple rule system and both can be implemented as computer programs.
Think of a grid (like a checker board) on which are placed a few checkers. Here are the rules to determine what the board looks like at the next "generation."
An empty "cell" will have a checker in it in the "next generation" if it has exactly 3 checkers in its immediate "neighborhood." (Each cell has 8 neighboring cells.) Think of this as the "birth" rule.
A cell that has a checker in it will be empty in the next generation (it will "die") if it has 1 or no checkers in its neighborhood or 4 or more checkers in its neighborhood. Think of this as under- or over-population.
An occupied cell with 2 or 3 neighboring checkers is happy as a clam and will survive and appear in the next generation.
Per usual, Wikipedia does it better so you are referred to
Wikipedia
After visiting the above link, the somewhat "dry" rule system will come alive and, if you "waste" enough time researching and "playing" with this, your "vocabulary" will increase and words like "gliders," "blinkers," "boats" etc. will take on new meaning.
Here's a pattern that
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repeats itself after 8 generations.
A page that contains a Java applet for Life follows.
Life
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