ImagesDescription
Mandelbrot Set

Close-up 'beauty shot' render of Mandelbrot set member cubes (Mental Ray).

Mandelbrot Set

Animation showing detail refinement as iteration limit is incrementally increased. Iteration limit is a threshold at which cubes are assumed to be Mandelbrot set members (3DS Max viewport).

Mandelbrot Set

Screenshot depicting development of Mandelbrot algorithm in MAXScript (3DS Max viewport).

The Mandelbrot set is an interesting phenomenon as it encapsulates an infinite number of elements. This makes it a good candidate for a data visualisation project. It can be defined with the following expressions:

$latex
M = \begin{Bmatrix}
c \in \mathbb{C} \mid \lim_{n \to \infty} Z_n \neq \infty
\end{Bmatrix}
&s=2 &bg=ffffff $

where:

$latex Z_0 = c &s=2 &bg=ffffff $
$latex Z_{n+1} = Z_n^2 + c &s=2 &bg=ffffff $

I set myself this project in order to learn MAXScript. The idea was to visualise the Mandelbrot set, a 2D entity, in a 3D environment. Rather than using the convention of pixels, I thought it befitting to instead use cubes, creating an unusual depiction of this mysterious fractal.

A detailed tutorial examining the implimentation of the Mandelbrot set in MAXScript can be found on my blog here: The Mandelbrot Set (MAXScript Fractal).