When were fractals "discovered"? By who?
There are
four people who made significant contributions to the development and experimentation
of fractals: Henri Poincaré, Pierre Fatou, Gaston Maurice Julia and his student, Benoit Mandelbrot.
Little can be found about Poincaré except that he first concieved them circa
1890. Afterwards, Fatou and Julia continued to elaborate on the discovery
and exploration of fractals. There is also little that can be found on
Fatou. Gaston Julia (1892-1978) was a French mathematician who studied Julia sets during the
early 20th century. However, Mandelbrot was the first to actually
"discover" fractals. While he was examining the shapes created
by Julia, he tried to classify the shapes by using a repeating equation and
"graphing" it. He worked for the IBM company and it was then
when computers were used to examine and develop fractals. Today, the most
recognized person who has worked with fractals is M.C. Escher.
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Is there a difference between Mandelbrot and Julia
fractals?
Yes, they have the same formulas, but their
starting values are different. In a complex plane, the various points are associated
with a Julia set, meaning that the Mandelbrot set acts as an "index"
for the Julia set. The formula can be the same
such as Zn+1= Zn2+C can be used to produce both
types of fractals. The difference is caused because the value of C is
fixed at a certain value and the value of Z is at the current point that you are
plotting, in the Julia Set. If the set is to be connected, the value of C
should be coming from the inside of the Mandelbrot set. Below is an example of the two fractals produced
using the formula mentioned above.
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How are the "fractals" interpreted?
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On the left is a fractal that we will use to help you interpret fractals, in general. The inside region is the darkest while the outside is the lightest. This is basically drawn on a Cartesian plane. The points on the graph are plotted according the the formula. Each time the formula is iterated, another point will be plotted making the black region the one with the most points. The other regions have fewer points. This pattern continues until the image shown on the left is created. |
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