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Fractal Image Algorithm

Started by Glass_Knife Aug 6, 2010 at 10:38 AM 3 replies 2.5k views

Original Post

Aug 6, 2010 at 10:38 AM

Long story short - A friend of mine at work belongs to a Fractal Society. I wanted to create and image of the Mandelbrot set. I've googled, but I can't find a simple code example. I see lots of math, and I understand how to create it (I think) but how is it turned into a visual example.

My coworker said something about a test for infinity, and keeping a count of every time a value is visited, but I still can't code up a program that makes an image.

Anyone with some guidance, I would appreciate it.

Thanks,

KulSeran

Aug 6, 2010 at 11:47 AM

From Wiki.
You are looking at the formula F(Z) : Z -> Z² + C. The objective is, for all pixels in your image, use the X,Y coordiate as a complex number C=X+Yi and test for several iterations with Z starting at 0, if Z = F(Z); escapes beyond 2. If it doesn't escape, it is the black center of the shape. If it does escape, use the number of iterations it took to escape to choose a color based on that speed of escape (or just make it white).

The complex math for F(Z) is fairly simple. You treat Z as x and y, and C as your X,Y coordintate, and F(x,y) becomes:
x_i+1 = x_i² - y_i² + X
y_i+1 = 2*x_i*y_i + Y
if ( x_i² + y_i² > 4 ) you escaped the disk, and should stop iterating this point. If after N iterations this never happens, then you are in the fractal.

--I miss Albuquerque. LA doesn't have good green chile.

Glass_Knife

Aug 6, 2010 at 12:12 PM

Quote:
Original post by KulSeran
--I miss Albuquerque. LA doesn't have good green chile.

I don't know what I'm going to do when I leave. The chile is soooo good.

Thanks for the info. I need to read it about 20 more times and code it up. I'm sure I'll have more questions after that...

Thanks Again,

CryoVenom

Aug 6, 2010 at 12:33 PM

I made a mandelbrot renderer, but I noticed that when I zoom in really far it becomes blocky. Is this normal for a basic mandelbrot renderer and is there a way to cause it to be "infinite"? Or is there specifically something I am doing wrong?

I can show the part where I calculate the value of the formula if someone requests to see it.

Moomin

Aug 6, 2010 at 12:57 PM

Quote:
Original post by CryoVenom
I made a mandelbrot renderer, but I noticed that when I zoom in really far it becomes blocky. Is this normal for a basic mandelbrot renderer and is there a way to cause it to be "infinite"? Or is there specifically something I am doing wrong?

I can show the part where I calculate the value of the formula if someone requests to see it.

Something is wrong, it is likely a precision issue. A quick way to tell if it is a precision issue would be to change from float to double, and record if the zoom level at which the 'blockiness' starts is increased.

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