POV-Ray : Newsgroups : povray.binaries.images : Pyramid fractal sort of.... : Re: Pyramid fractal sort of.... Server Time
4 Oct 2024 03:16:45 EDT (-0400)
  Re: Pyramid fractal sort of....  
From: Chris Maryan
Date: 23 Apr 1999 23:22:06
Message: <37212B87.C85ED3CB@geocities.com>
In 2D, the recursive triangle shape thing is properly called
Sierpinski's Gasket, alternatively Sierpinski's Triangle. It is closely
related to Pascal's Triangle, a series of numbers in a triangle pattern
used for various mathematical things. If you colour every odd number in
pascals triangle black and all the even ones white, you get this
pattern. In 2D, there are dozens of unique techniques for getting this
shape (including fractal trees, it may be possible in 3D using Giles'
macro although I haven't looked at it).

For reference, Pascals Triangle:

		1
               1 1
              1 2 1
             1 3 3 1
            1 4 6 4 1
And so on...
(And if you can't figure out the pattern, think harder :-)
The area of your triangle approaches 0, and I can't remember if the
perimeter is finite or goes to infinity.


Anders Haglund wrote:
> 
> Hi everyone.
> 
> Here is a small cool 3D fractal I slamed together. I don't know what it's
> called but I recon it's closely related to the fractal in the "fractal
> cheese" posting.
> Don't complain about the floor! =)
> Anyway, enjoy or what ever...
> 
> /Anders
> 
>  [Image]

-- 
Chris Maryan
mailto:cma### [at] geocitiescom
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