Some fractals

“For much of my life there was no place where the things I wanted to investigate were of interest to anyone.“
- Benoit Mandelbrot

“Nobody will deny that there is at least some roughness everywhere.”
- Benoit Mandelbrot

“There is a joke that your hammer will always find nails to hit. I find that perfectly acceptable.”
- Benoit Mandelbrot

“When the weather changes, nobody believes the laws of physics have changed. Similarly, I don't believe that when the stock market goes into terrible gyrations its rules have changed.”
- Benoit Mandelbrot

$It’s a fractal world...$

A Mandelbrot Set Zoom

Orbit of a Point in the Mandelbrot Set..near a ten-ball?..

Web Diagram Showing Chaos

$Ron's old book on fractal geometry & chaos (link below)... A high school text / lab manual for discovering patterns and principles of fractal geometry and chaos science. For high school students...perhaps people of any age, it requires readers to experiment as they go along. Here is a link to some excerpts; the book is currently out of print but the author is considering resurrecting it as a page on this web site (don’t hold your breath, that is a lot of work) Fractals in Your Future A Primer on Theory and Applications of Fractals and Chaos -- by R. S. Lewis Another book on fractals that Ron is involved in (links below)... This book is related to a ‘it’ll-never-happen-in-your-lifetime-but-did’ experience. I had the temerity to write Benoit Mandelbrot, the Father of Fractal Geometry, and tell him about my high school course and my book (above). I got encouraging replies back, my name got forwarded to others, then I find myself, in December 1997, on a plane to Connecticut, USA, to participate in a symposium at Yale University, of teachers of various grade levels, who have been introducing their students to fractal geometry. Our host is Michael Frame, professor at Yale, with his own wonderful fractals course, an excellent author of books on the subject. Every night we dine with professor Mandelbrot. One day, Mandelbrot gives a few of us his personal tour of the Yale campus. What a wonderful time! The event lasts about four days, and the participants, and a few others who could not attend, are invited to contribute to a book. The book is to be published by the MAA (Mathematical Association of America), and Mandelbrot is considering asking his friend, Arthur C. Clarke, to write the forward, but that doesn’t happen. The book however gets published in 2002. Here are a couple of links to it: Fractals, Graphics, and Mathematics Education My chapter (12): Exploring Fractal Dimensions by Experiment Brian Kaye, Ron’s mentor... I will stop short of saying that my work on fractals was ‘inspired’ by Dr. Kaye, because that would be presuming my work to be ‘inspired’. But without Dr. Kaye there would have been no fractals project nor anything resembling that, and my life from 1987 on would have been much different. The late Dr. Brian H. Kaye, professor of physics at Laurentian University in Sudbury, Ontario, Canada was a gifted researcher and teacher, whose boundless energy, intelligence, and ability to bring subjects down to the level of his audience touched many. I am in awe of my experiences as his student and protégé, to this day. I’ll leave you now with a link to an e-book version of one his books on fractals: A Random Walk Through Fractal Dimensions$ shapeimage_3_link_0