Welcome to Fractal Forums

Fractal Math, Chaos Theory & Research => Mandelbrot & Julia Set => Topic started by: hoddie54 on March 12, 2012, 11:50:59 PM




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.