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Author Topic: Real life application of the Mandelbrot and Julia Set  (Read 28052 times)
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grd_erik
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« on: April 24, 2011, 01:39:46 PM »

All of the Mandelbrot set and Julia Set is wonderfull with the maths behind it. But what do they actually use it for in real life? All i have heard is people are able to make computer generated mountains because it has a repeating pattern but other than that nothing and i am sure there is more to it. So can anyone enlighted my kowledge and show me what are the real life application of the Mandelbrot Set. Thanks for helping.
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Sockratease
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« Reply #1 on: April 24, 2011, 02:04:42 PM »

Hello and welcome to the forums.

The Mandelbrot set in particular - not sure of any applications.

Fractals in general though - MANY uses!!

Fractal shaped antennas make your cell phones possible  (YES they were not possible before the introduction of this idea). 

Chaos theory is what fractals are all about, and that is at the core of most Cosmological Models describing our entire Universe on both the scales of the Very Large and the Very Small  (the problem areas in Grand Unification Theory - so they may well help with that issue).

People have found fractal geometry useful for all sorts of things from biology to physics to cosmology to even the stock market.

But their single most useful contribution to society is that they makes purty pixtures.  You still have time to enter some in our Annual Contest too!

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grd_erik
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« Reply #2 on: April 24, 2011, 07:36:59 PM »

Interesting stuff, i'll research them

What is this annual competition?
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Lee Oliver
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« Reply #3 on: April 24, 2011, 08:15:56 PM »


Fractal shaped antennas make your cell phones possible  (YES they were not possible before the introduction of this idea). 


This is a very simple application, yet satisfying nonetheless.  I made one of my old radios work better by far with a crude koch curve.
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Sockratease
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« Reply #4 on: April 24, 2011, 08:20:11 PM »

http://www.fractalforums.com/index.php?action=gallery;cat=52

That's the competition section of the gallery.  Once a year we have a competition and users vote the winners. 

Maybe this will explain it:

http://www.fractalforums.com/fractalforums-com-spring-2011-fractal-art-competition/fractalforums-com-spring-2011-fractal-art-contest/

That's got the rules.

And this is the banner I made before we renamed it from Spring Competition to Annual Competition!

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grd_erik
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« Reply #5 on: April 25, 2011, 03:33:12 AM »

Cool stuff, i mite enter into the competition.

If anyone else has any other real life applications i would love to hear of them.
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hobold
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« Reply #6 on: April 29, 2011, 12:30:31 AM »

Fractal geometry is being applied to deal with natural fractals mostly. For instance veins and arteries form fractal trees, some mineral deposits are distributed fractally through the soil, and the stock market (perhaps not quite a natural phenomenon) behaves according to fractal laws. As far as I am aware, there exist (or at least used to be at some point) software applications to solve specific problems in these three fields.

None of these cases involve classical Mandelbrot or Julia sets, though.
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makc
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« Reply #7 on: April 29, 2011, 01:18:00 AM »

apparently, Mandelbrot set was just a side effect of his work in complex dynamics. to quote wiki,
Quote
the study of dynamical systems defined by iteration of functions on complex number spaces.
what particular system was studied by Mandelbrot could be mentioned in his original work "Fractal aspects of the iteration of z=λz(1-z) for complex λ,z", but I can't find free pdf anywhere.
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makc
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« Reply #8 on: April 29, 2011, 01:26:12 AM »

ha, according to wiki it was actually not Mandelbrot who discovered the set embarrass here is the paper with 1st rendering ever.
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Don Whitaker
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KitchenDon
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« Reply #9 on: April 29, 2011, 02:33:47 AM »

I think fractal math is also involved in JPG, MP3, MPG and other digital compression. http://en.wikipedia.org/wiki/Fractal_compression
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grd_erik
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« Reply #10 on: April 30, 2011, 10:04:27 AM »

interesting stuff, thanks for the submissions.

Always nice to know that there is a fractals inside of my phone or in my vain structure.
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LMarkoya
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« Reply #11 on: June 10, 2011, 10:49:15 PM »

The Nova special on fractals had some practical uses. Including the design of sound barriers for next to highways, whicch became immensely more efficient with a fractal pattern in the cement
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jehovajah
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« Reply #12 on: July 02, 2011, 05:06:54 AM »

Just as a flag has no real practical use the julia and Mandelbrot sets are identifying and rallying symbols for a new way of understanding geometrical ,dynamic relationships.

Their fundamental resonance within our neurology is the source of their importance. While not actually describing the real cosmology, they indicate that cosmological concepts are ultimately based on simple laws of motion and relation. They form an easily recogniseable benchmark, and "generated" the sophisticated graphing tools called fractal generators.

I feel that the fractal generator is an underrated tool of great significance and is probably the real product of the mandelbrot and julia sets. Lazarus Plath has taken it several stages further but does not eem to realise the significance of what he has done.
Finally the Manddelbrot set made complex numbers real in a way no other application has, even the phase mathematice involved in signal processing.

With 3d printing techniques i feel that a print out of the Mandebulb may reveal other exotic uses in electronics.
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