The Mandelbrot Set
Cute, ain't it! This "fractal" image was discovered by Benoit Mandelbrot. It is formed by plotting randomly generated dots onto a matrix using a very simple geometric algorithm. Colours are assigned to the dots based on the speed at which they diverge from zero during generation. As you "zoom" into any area of the set, new and unique patterns emerge. In fact, it goes on generating to infinity.
Mandelbrot, born in Poland in 1924, showed how fractals can occur in many different places in both mathematics and elsewhere in nature.
A truly beautiful (and very interesting) IMAX movie has been produced by 'Films for the Humanities and Sciences, Princeton, New Jersey' called "Fractals: The Colors of Infinity", presented by Arthur C. Clarke. The movie takes you on an amazing computer-generated video journey deep inside the Mandelbrot set. It also explains how fractal geometry pervades all forms of life, dictating the shapes of ferns, trees and even the coastal contours of countries. And to top it all, the accompanying music is composed and played by David Gilmore of Pink Floyd! [Friends and relatives can request a copy for PC play in exchange for food :) ]
The fractal images are an illustration of "Chaos Theory". If you'd like to know more about the Mandelbrot set, fractals, and chaos theory in general take a look at James Gleick's 'Chaos: Making a New Science'. I have owned a hardback copy for many years, but it is available in paperback from Amazon books and not too taxing for the non-mathematician!
OR, if you really want to have some DIY fun, why not visit the Software Engineering Laboratory at the National Technical University of Athens , and live the experience!
Benoit Mandelbrot outside the Newton Institute at Cambridge
You do the math!!
A Guide for People with little Math Experience
Courtesy of David Dewey
"The Mandelbrot set is a mathematical set, a collection of numbers. These numbers are different than the real numbers that you use in everyday life. They are complex numbers.
Complex numbers have a 'real' part plus an imaginary part. The real part is an ordinary number, for example, -2. The imaginary part is a real number times a special number called 'i', such as, 3i. An example of a complex number would be -2 + 3i.
The number 'i' was invented because no real number can be multiplied by itself and result in a negative number. This means that you cannot take the square root of a negative number and get a real number.
When you take the square root of a number, you find a number that can be squared to get that number. The number i is defined to be the square root of -1. This means that i squared is equal to -1.
So when you square an 'imaginary' number you can get a negative number. For example, 3i squared is -9". Thanks to David Dewey at: http://www.ddewey.net/mandelbrot/
IF, LIKE ME, YOU FIND ALL THIS STUFF INTERESTING, ALSO LOOK UP "JULIA SETS" ON THE WEB AND DISCOVER ANOTHER WORLD OF FRACTALS. EVEN IF YOU CAN'T STAND MATHS, YOU CAN CERTAINLY ENJOY THE PRETTY PATTERNS!
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