Mandelbrot with 3DickUlus averaging coloring methodThe Stars AlignNew Videos
The Stars Align
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Description: A modified version of the Buddhabrot function
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Posted by: AranLeer March 13, 2020, 01:25:16 PM

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pauldelbrot
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March 13, 2020, 01:54:36 PM
z6 + c Buddhabrot?
AranLeer
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March 13, 2020, 02:00:41 PM
It is a Z6 Buddhabrot, but with a per-iteration "post-effect" of moving the x-coordinate of the trajectory by -1.


So, like this:

Code: [Select]
for(i=0;i<maxIter;i++){
r=Math.pow(r,6);
th1=th1*6;

a = r*Math.cos(th1)-1;
b = r*Math.sin(th1);
a+=ai;
b+=bi;

r = Math.sqrt(a*a+b*b);
th1 = Math.atan(b/a);

//Update Pixel
}
pauldelbrot
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March 13, 2020, 02:18:06 PM
That's the same as translating c by one, so, just translating the image itself by one, isn't it?

Hmm. Code looks like Java. Converts to polar and then cartesian again every iteration -- is that actually more efficient once the power gets that high?
AranLeer
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March 13, 2020, 03:05:29 PM
Yes, it is Java code.
That's just the language I am most familiar with, and it's fast enough for tinkering with. :)

As far as converting between polar and cartesian each iteration - I normal keep everything in cartesian coordinates, as it is much faster. But I've been playing around with different types of "post-affects" in fractals, and for this particular image I was interested in how "post-affects" would affect polar coordinate versions of the fractal. So I do the primary calculations in Polar, but have to convert to cartesian to find the pixel's x and y coordinates (since for Buddhabrot the pixels need to be updated each iteration).

As far as the "post-affect" being the same as adjusting the C value - Yes, it is the same as shifting the C value. In this case it was still somewhat novel because it was being used with Polar coordinate calculations - but normally I have been doing some "post-affects" that are more complex, such as adjusting by a dynamic value based on the iteration number, or even doing rotations each iteration. These have produced a few other interesting images I have uploaded previously (like the "Fluffybrot" and "Cyclops" images). But yes - as for this image, it was probably not worth mentioning it as a "post-affect". :)


Also - after doing a little more testing - I found out the reason I was getting the interesting "stars" in this picture is because I was using the wrong initial condition for the fractal. I had been setting the initial Polar Coordinate to some value other than (0,0), and because of that, when I did the "-1" as a "post-affect", it was actually making a unique difference other than just shifting the C value by -1. So if I correct the issue and put the initial coordinate to (0,0), then changing the C value is the same as updating the x coordinate by a fixed value each iteration.

Thanks for your input, or I would probably have not figured that out :)

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