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

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).

Zoomed-out render showing how small cubes compose an intricate fractal (Mental Ray).

Animation providing a holistic vantage point of the fractal (3DS Max viewport).

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

￬ View Description

Personal Work
Workflow: C++ prototype ➞ Implementation of Cube Array ➞ Implementation of Per-Cube Loop in which Mandelbrot Algorithm Nests ➞ Optimisations to Exclude Creation of Unnecessary Cubes ➞ Special Effects & Material Setup

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:

$M = \begin{Bmatrix} c \in \mathbb{C} \mid \lim_{n \to \infty} Z_n \neq \infty \end{Bmatrix}$

where:

$Z_0 = c$
$Z_{n+1} = Z_n^2 + c$

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). A stripped-down version of the script (featuring only the Mandelbrot algorithm and no optimisations/special effects) is provided below in MS format.

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