| Julia and the third dimension | |
For some obscure reasons
I did not get started for quite a time on the tree dimensional Julia pictures.
Although I had created lots of two dimensional images, I could not imagine what
happens on the z axis. So, best is to write a program that shows it.
The following pictures show on the left hand the selection of a location on
the Mandelbrot set, in the middle the corresponding Julia figure in 2D and on
the right in 3D. At least I was clever enough to provide output of 3D as well
of 2D in this same program.
Selection |
2D |
3D |
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In this first case we selected a dot within the standard (2. potency) set leading to the other two images which seem OK.
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If we select an dot within the green edge around the set leading to a reasonable 2D image, but 3D is rather a mess. So I finally understood what people talked of roughness of the 2D images - with my sore eyes I could not get it.
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And if finally you select a dot far outside the set you get pretty, but very modest pictures. Seeing this you may understand the use of "Fatou dust" while meaning Julia things: Every dust particle on the complex plane leads to an image.
| images | |