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Mandelbrot Set

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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.

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Amazing

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

mmm

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

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?

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.

hmm

not fun... but trippy as fuck haha. enjoyed it.

Credits & Info

Views
4,572
Faves:
3
Votes
11
Score
3.82 / 5.00

Uploaded
Jun 28, 2009
1:19 PM EDT
Genre
More Games