Robert Dawson wrote:

> Greg M. Johnson <gre### [at] my-dejanewscom> wrote in message
> news:37E2407B.F551ABC8@my-dejanews.com...
> > Why can't we implement a Sierpinski pattern in povray?
> >
> > As I understand povray, for some of the more mathematically complicated
> > thingies,  such as isosurfaces of complex equations and the bozo or
> > Mandelbrot patterns,  the complexity of the feature depends on the
> > density of rays hitting it.  For example, the computer doesn't have
> > stored the "entire" Mandelbrot set at all magnifications, but merely
> > calculates the pattern at the place where a traced ray hits the object.
> > Thus, there are few practical limits to zooming in (reducing camera
> > angle) to see smaller and smaller regions of the Mandelbrot pattern.  Am
> > I right so far?
> >
> > It's pretty hard for me to construct a Sierpinski object beyond a half
> > dozen orders of scale. Isn't this just another mathematically
> > complicated thingy that povray can solve procedurally?
> >
> > So why can't we put a Sierpinski pattern in povray?
>
>     Undoubtedly, it could be done. However, it could also be done as a macro
> rather easily, and there are so many variuations on the Sierpinski theme
> that a good macro, editable by the user, would be far more flexible.
>
>     More to the point: how about a Julia set pattern? The Julia sets, being
> more repetitious, are a better pattern for most purposes than the Mandelbrot
> set. The periodic-function variants are even better for such a purpose.
>
>     -Robert Dawson

Perhaps even a more generalized fractal pattern, something that would allow you
to define with some flexibility the way in which the fractal was generated.  I
think that this could have the potential to be very powerful.  It might,
however, also be very difficult to learn how to use properly.

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