## Mandelbrot Set

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rated 2.00 / 5 stars
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## Credits & Info

Jun 28, 2009 | 1:19 PM EDT

#### If you liked this, check these out!

A lot of people have said they don't know what it is. So here is an explanation of what it is, and how it is programmed:

The Mandelbrot set is a fractal. It is an infinitely complex structure. You can zoom in and in and in on it and it will never simplify. The way it is defined has a lot to do with complex numbers.

A complex number is a number with a 'real part' (just a normal number, like 1, -66.8, Pi etc.) added to an 'imaginary part' (this is a real number multiplied by the square root of minus one).

The "absolute value" or "size" of a complex number is the square root of the sum of the squares of the real and imaginary parts. | a+bi | = sqrt(a²+b²).

Each pixel on the screen can correspond to a complex number (i.e. the pixel at (13, 66) corresponds to 13+66i ,where 'i' is the square root of minus 1).

If you take a complex number C, say 1+1i, then add its square to it, then a new complex number Z is created. (in this case -11+7i which has an absolute value of 170). you can then square Z and add C to get a new value for Z. You can then square the new value of Z and add C to it again etc.

This can be repeated as an iteration, written as: Z => Z²+C. So C is a constant, and Z is a variable which initially starts at 0, and then changes every iteration. Here is the clever part:

The colour of each pixel on the screen is determined by the amount of iterations needed before the absolute value of Z becomes larger than a predetermined value, with the value of C depending on the
X and Y co-ordinates of the pixel. If, after many many iterations, the absolute value of Z is still below the predetermined value, then the pixel is coloured black.

This explanation probably sucks for anyone who doesn't already understand it., but at least I tried.

## Reviews

#### TexasTerri

##### Rated 5 / 5 stars2009-10-13 20:58:59

Amazing

ive been looking for this program since i saw it on a fractal documentary, thanks for posting this!

#### dondido

##### Rated 5 / 5 stars2009-06-28 17:06:39

mmm

fractals fractals whoop whoop 5 out of 5!
I dont think many people can understand the infinite magic of it....

#### spazzman37

##### Rated 2.5 / 5 stars2009-06-28 15:54:48

IDK

I really don't get the point of this. I admit it was abit interesting ,but still have better things to do. I don't think you should make another game like this, it was okay but it's not something I would look froward for another one. Only advice is try a different type of game. I give it a five for a good try and in hope your next game will be better.

georgepowell responds:

It isn't a 'game' in the normal sense. It is more of a tool. I make things like this because I am a programmer, not an artist. Maybe this is the wrong place to be uploading them?

#### LeTapir

##### Rated 4.5 / 5 stars2009-06-28 14:34:31

Pretty well done

The problem with fractals is... well they are fractals thus making them impossible to draw. To those who don't know what a fractal is, it's a figure that repeats a portion of itself (idk how to explain this in english) to the infinity. You can't really draw infinity. So the only way to make this wasn't with a picture that you can zoom, but with really complex programming, so i'm gonna give you a 10 and because it was fun to see. As said xanadu32, you should tell people this is a fractal, otherwise they will just blam it, when it's a very nice piece of work.