>   A "regular" 2-dimensional julia uses complex numbers. If you are interested,
> the formula is the following:
> 
>   For each point c in the complex plane, the julia set (let's call it J) will
> be:
> 
>   J = { c |  lim   Z(n) != inf }
>             n->inf
> 
> where:
> 
>   Z(0) = c
>   Z(n) = Z(n-1)^2 + Y
> 
> where Y is a complex number (in a Mandelbrot set it will be c itself, in a
> Julia set it's a chosen complex number which doesn't change).
> 
>   When the Julia set is displayed in the complex plane (it's usually
> denoted so that the x-axis in a cartesian system denotes the real part of
> the number and the y-axis denotes the imaginary part) it forms the peculiar
> shape you know.
>   (The colors displayed outside the set are not part of the set but are
> created by a simple trick.)
> 
>   Now, the 4-dimensional julia uses either hypercomplex or quaternion
> numbers instead of complex numbers.
>   The formula is exactly the same as above, the only difference being that
> hypercomplex and quaternion numbers have 4 parts instead of 2.
>   This means that the set will be formed in the 4-dimensional space.
>   The difference between hypercomplex and quaternion numbers is that for
> numbers with more than 2 parts some mathematical operations (such as
> multiplication) are not unambiguously defined. Hypercomplex and quaternion
> numbers use different type of multiplication.
> 
>   Since the set has 4 dimensions, a 3-dimensional "slice" has to be taken
> from the set in order to represent it in 3D space.
>   This is similar to cutting a 3D object with a plane and getting a 2D shape
> in the plane. But instead of making a 2D slice from a 3D object, we are
> making a 3D slice from a 4D object.
>   It's not possible to represent a 4D object in itself because our brain
> can't handle that information. This is why we need a 3D slice of that object.

Cool, Thanks a lot!

> : For the 2D fractals, I would prefer to construct them myself...
> 
>   Why, when there's already a pattern for that?

Because, I could play with colors, and paterns and shape, make it move, etc... 
I would do this using OpenGL, so it would be fairly fast, fullscreen and quite
amazing!

Thanks,
	Simon
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| Simon Lemieux           | Website : http://www.666Mhz.net  |
| Email : Sin### [at] 666Mhznet | POV-Ray, OpenGL, C++ and more... |
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