Title: Good coordinates for Mandelbrot zooms? Post by: sonofthort on October 05, 2010, 08:48:53 PM I'm working on a fractal project using CUDA, which is soo smokingly fast that I am able to render 800x800 zooms in real time ;D. I was wondering, are there any websites out there that might list some interesting coordinates to zoom into, or would anybody be willing to share some?
Title: Re: Good coordinates for Mandelbrot zooms? Post by: bib on October 05, 2010, 09:54:06 PM Near the border :D
No, seriously it all depends on what YOU find interesting. I think that somebody posted here (or provided a link) some well-known techniques to find interesting places to zoom in, but I have no clue where to find the thread. The fun thing about the Mandelbrot set is to explore it, and then, after some hours of exploration, you will find intuitively where to find minibrots and where to zoom... Title: Re: Good coordinates for Mandelbrot zooms? Post by: sonofthort on October 06, 2010, 12:37:17 AM I'm probably going to make a mode where is constantly zooms in at the point your cursor corresponds to with the ability to save the final coordinate.
However, we would like to do some deep zooms which could take weeks to render, meaning the guess and check method is probably not the best way to go, especially since performance will take a huge hit once the zoom is far enough that arbitrary precision kicks in. One method I considered was looking at orbit cycles to find coordinates that would work for deep zooms. Orbits starting from points within the set eventually cycle between a set of points (or just settle on one point). My theory is that points which have really large cycles would be good for deep zooming. I am basing this off of using programs which draw the orbit paths for any point on the set which your cursor corresponds to. The Mandelbrot set is made up of a lot of circles and cardioid, and it seems that the smaller the circle/cardioid, the higher the number of orbit cycles it produces. Title: Re: Good coordinates for Mandelbrot zooms? Post by: lkmitch on October 06, 2010, 01:54:21 AM Points on the boundary of the Mandelbrot set generally have the most interesting orbits. The easiest boundary points to compute are:
* the spike along the negative real axis * the boundary of the main cardioid: r = (1 - cos(theta))/2, x = r*cos(theta)+0.25, y = r*sin(theta) * the boundary of the period 2 disk: r = 0.25, x = r*cos(theta)-1, y = r*sin(theta) Title: Re: Good coordinates for Mandelbrot zooms? Post by: sonofthort on October 06, 2010, 02:08:48 AM Ty ^^ I'll have to test those out when I get a chance. |