Title: Changing Mandelbrot Formula Post by: hoddie54 on March 12, 2012, 11:50:59 PM Using a custom fractal program I have changed the formula from Zn = Zn-12 + C to Zn = Zn-1K + C, where both C and K are constants (K is real and an integer). So for example the formula could be Zn = Zn-14 + C, and then it renders it as a Mandelbrot.
My question is a possible explanation for something very strange that I've encountered and I'm wondering if it is just a programming error or something in the fractal itself. Upon increasing the value of K to something like 12, a strange circle appears. Similarly if I decrease the zoom on the normal Mandelbrot (around 10^-38), I also get the circles. Here are some pictures - I'll make more sense:[spoiler] Normal Equations: (http://screensnapr.com/e/yUnyrx.png) Zoom in on this circle (Normal Equation): (http://screensnapr.com/e/Ccbdis.png) Where K = 10: (http://screensnapr.com/e/759Lkm.png) Where K = 10, and it is zoomed in onto the circle: (http://screensnapr.com/e/s0GRwo.png)[/spoiler] Title: Re: Changing Mandelbrot Formula Post by: lkmitch on March 13, 2012, 04:55:01 PM I'm guessing programming error, possibly related to the bailout. Or maybe an overflow. The nine-lobed critter for k=10 looks correct, though. |