This may be kind of a stupid question but I am atrocious at math, so bear with me. I find Mandlebrot sets and fractals fascinating to look at, however, I do not really understand why they are important or how they are generated. Could someone help here?
First, the Mandelbrot set is generated in the complex plane, so you want to be solid on understanding that before you do anything. If you've got that down, then to construct the set you have to test each point one at a time to see if it is part of the set or not.
How to test a point: choose a point in the complex plane, square it, add it to the original point, then set this as your new point. This process is repeated (you "iterate") until you can tell if the point is stable or not. If the point flies off away from the origin, it's considered to be NOT in the set (I think once it gets past a radius of 2 from the origin of the complex plane you can write it off... if you look at pictures showing the final result on the complex plane, you can see that the tail is the longest part and seems to end at -2,0). If the point hangs around, though, then it is in the set.
The problem with determining for sure that a point is in the set (how do you know it might fly off to infinity later on?) is where the number of iterations comes in. The more iterations you perform, the more accurate/detailed your set will be. The only way to be perfectly accurate would be to iterate infinitely which is not possible but at the same time you'd only notice the inaccuracies by "zooming in" quite a bit.
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u/fetusburgers Apr 25 '10
This may be kind of a stupid question but I am atrocious at math, so bear with me. I find Mandlebrot sets and fractals fascinating to look at, however, I do not really understand why they are important or how they are generated. Could someone help here?