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Welcome to Fractal Forums > Fractal Math, Chaos Theory & Research > General Discussion > What's up with these circles in the Nova fractal?
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Author Topic: What's up with these circles in the Nova fractal?  (Read 2555 times)
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panzerboy
Fractal Lover
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Posts: 242
« on: October 04, 2012, 10:17:34 PM »
These strange circles appear in the Nova fractal.

<a href="http://www.youtube.com/v/_3r2GMYfQLE&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/_3r2GMYfQLE&rel=1&fs=1&hd=1</a>

I made my own video to confirm this wasn't a fake.

<a href="http://www.youtube.com/v/Azun3fxg8ik&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/Azun3fxg8ik&rel=1&fs=1&hd=1</a>

You can also produce these circles in Ultra Fractal
Interesting that the smooth colouring shades the circle, suggesting some variation in the iterations?
The 2nd picture is off to the left zoomed in a bit more to show that its not a precision related issue.

* NovaDot65.jpg (87.67 KB, 640x480 - viewed 400 times.)

* NovaDot2.jpg (93.8 KB, 640x480 - viewed 420 times.)
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Tglad
Fractal Molossus
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Posts: 703


WWW
« Reply #1 on: October 05, 2012, 11:46:16 AM »
No idea, but there seem to be circles in the zoomed out version of two of the example fractals on the wikipedia page: http://en.wikipedia.org/wiki/Nova_fractal

If you plot the path of a pixel inside the circle compared to one outside, you might get an idea why. On the mandelbrot set I think the circles correspond to different cycle lengths, e.g. bouncing in a triangle for the 3rd largest circle.
Let us know if you find out!
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panzerboy
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Posts: 242
« Reply #2 on: October 05, 2012, 10:29:48 PM »
Quote from: Tglad on October 05, 2012, 11:46:16 AM
...
If you plot the path of a pixel inside the circle compared to one outside, you might get an idea why.
...

You can Ctrl-Shift click in Fractal Extreme to view the 'calculation path'.
Unfortunately that doesnt scale when you've zoomed in so all you see is a line going off the window.
Can I do something similar with UltraFractal?
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panzerboy
Fractal Lover
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Posts: 242
« Reply #3 on: October 05, 2012, 10:41:12 PM »
I have it!
The 'bailout' parameter in Ultra Fractal is small 0.00001 for the Nova.
Making this value larger increases the size of the circle, making it smaller decreases the size.
In Fractal Extreme the 'overflow point' in the advanced settings is set to 2, aletring this has no effect.
I suspect that the Nova plugin for Fractal Extreme is ignoring the overflow point parameter as there is only 1 digit of decimal for entry.
Internally it probably has a fixed bailout of 0.00001
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