"Craig Lindley" <cal### [at] gmailcom> wrote:
> Hello,
>
> I came across the attached image the other day that I thought was beautiful so I
> decided to look at raytracing again. I hadn't done any raytracing since about
> 1993 so the POVRAY program has changed quite a bit. I am using the 3.8 version
> of POVRAY and it is amazing. I retraced one of my old images that took 33 hours
> in the 1990's and today on my Mac it took about 10 minutes.
>
> Anyway. I would like to understand how this image was produced because I would
> like to do something like it for this years Christmas card.
>
> It seems to be made up of Fibonacci spirals but I am not sure. I looked at the
> POVRAY documentation for these types of spirals but I cannot seem to duplicate
> the image accurately. I would guess that each color is its own Fibonacci spiral
> but how they are positioned so they don't interfere with each other escapes me.
>
> Any help or suggestions would be appreciated. If anyone has access to the actual
> POV file for this image I would love to have it.
>
> Thanks in advance.

Welcome back to POV-Ray and raytracing.  :)

Well - they are spirals, whether or not they are Fibonacci or Golden spirals or
logarithmic or Archimedean spirals is anyone's guess.

Get yourself an equation or algorithm for a spiral and make the first one - NOT
starting at the origin, but a bit off to the +x side.
Then you can either generate a new spiral starting with a sphere that's first
rotated around the origin a bit, or just generate the same spiral as a union,
and rotate the whole thing.
I'd start by just drawing a circle, and based on the fact that you can go once
around a circle with 6 of its radii, then you can do some basic geometry/algebra
and figure out what the diameter of each sphere should be if their centers lie
on a given circle.
Step out away from the origin and figure out a second circle that have spheres
that will be tangent to the first, and you'll likely be able to come up with an
algorithm or formula to iterate out.

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