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Thread: Mandelbrot set!
 05112012, 05:58 AM #1
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Mandelbrot set!
Hey guys,
I haven't been doing any interesting projects lately (besides class projects, which aren't very interesting). So, as an exercise I decided to tackle mandelbrot sets. It's actually been quite simple and the majority of my code was representing Complex numbers. My program is the inefficiency I am running into.
I am wondering how to make a quicker method to test for convergence. Here is what I've got:
Java Code:private boolean converges(ComplexNum input){ int count = 0; ComplexNum start = input; ComplexNum zCurrent = new ComplexNum(); ComplexNum zNext = new ComplexNum(); while(zCurrent.getReal() < 2 && zCurrent.getImaginary() < 2 && count < 45){ zNext = zCurrent.mult(zCurrent); zNext = zNext.add(input); zCurrent = zNext; ++count; } if(zCurrent.getReal() < 2 && zCurrent.getImaginary() < 2){ return true; } return false; }
Java Code:public void generateSet(){ for(double i = 2; i < 2; i += .001){ for(double j = 2; j < 2; j+= .001){ ComplexNum current = new ComplexNum(i, j); if(converges(current)){ set.add(current); } } } }
Picture for anyone interested:
Thanks in advance.Last edited by sunde887; 05112012 at 06:06 AM.
 05112012, 08:03 AM #2
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Re: Mandelbrot set!
There's a horizontal axis of symmetry (i.e. if (x,y) is an element of your set so is (x,y)); this speeds up the entire thing by a factor of 2.
kind regards,
Jocenosillicaphobia: the fear for an empty beer glass

Re: Mandelbrot set!
I don't know about speeding up the algorithms, but I do know that the images of this and the corresponding Julia sets get a whole lot more interesting when you assign different colors for different speeds of divergence (not sure if that is the right word), as my forum image demonstrates.
 05112012, 09:16 PM #4
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Re: Mandelbrot set!
cenosillicaphobia: the fear for an empty beer glass
 05112012, 09:49 PM #5
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Re: Mandelbrot set!
b.t.w. your stop condition in the while loop isn't correct; it should be c < 2, i.e. for c == a+b*i, a*a+b*b < 4
kind regards,
Joscenosillicaphobia: the fear for an empty beer glass
 05122012, 03:01 AM #6
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Re: Mandelbrot set!
 05122012, 10:12 AM #7
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Re: Mandelbrot set!
Have a look here.
kind regards,
Joscenosillicaphobia: the fear for an empty beer glass
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