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Author Topic: Changing Mandelbrot Formula  (Read 2095 times)
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hoddie54
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Posts: 2


« 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:

Zoom in on this circle (Normal Equation):

Where K = 10:

Where K = 10, and it is zoomed in onto the circle:
[/spoiler]
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lkmitch
Fractal Lover
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Posts: 238



« Reply #1 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.
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