Benoit Mandelbrot Dies at 85
It was probably in 1983 that I got my first depiction of the Mandelbrot set. I have just installed a black-and-white IBM PC with the screen resolution of 320×200, spent 5 minutes writing a Basic program and let it run for the whole night. In the morning, the results of my very first program written for my very first personal computer were up there on the screen - there were no screen savers at the time. Although black-and-white and rather uncouth, the image was charming in that it was a result of running a simple iterative process involving a quadratic polynomial. It went beyond a mere surprise that such a well studied function held hidden such an intricacy of design.
A generation later it may be hard to imagine the popular excitement induced by the spread of Mandelbrot's concept of fractals. Now that, as was famously proclaimed by M. Barnsley, fractals are indeed everywhere, and have entered the mainstream of science and technology, the excitement has subdued.
There is a lot of information about fractals at the Interactive Mathematics Miscellany site.
- Mandelbrot Set and Indexing of Julia Sets. This is actually how Mandelbrot came across his eponym - by trying to classify various Julia sets.
- Iterations in the Mandelbrot Set. This is an illustration of one of the better understood properties of the Mandelbrot set. How the iterations depend on the starting point.
- Color Cycling on the Mandelbrot Set. Color cycling is what endeared the fractals on the broad public. Although, extraneous to the fractal proper, the cycling on the level curves adds to the excitement.
- Fractal Curves and Dimension. Fractal dimension is the basis for understanding fractals and has motivated Mandelbrot to coin the term itself.
- For more check a more complete set of articles and interactive demonstrations.
References
[amtap book:isbn=0120790629]
[amtap book:isbn=0716711869]
[amtap book:isbn=0387966080]
[amtap book:isbn=0387979034]
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