The Bodaciously Excellent Blog of Doctorwhen

Mandelbox Zoom

Mandelbox Zoom

An amazing zoom on the Mandelbox made with Mandelbulb 3D v1.53 and VirtualDub.

In mathematics, the mandelbox is a fractal with a boxlike shape found by Tom Lowe in 2010. It is defined in a similar way to the famous Mandelbrot set as the values of a parameter such that the origin does not escape to infinity under iteration of certain geometrical transformations. The mandelbox is defined as a map of continuous Julia sets, but, unlike the Mandelbrot set, can be defined in any number of dimensions.

The iteration applies to vector z as follows:

function iterate(z):
    for each component in z:
        if component > 1:
            component := 2 - component
        else if component < -1:
            component := -2 - component

    if magnitude of z < 0.5:
        z := z * 4
    else if magnitude of z < 1:
        z := z / (magnitude of z)^2
    z := scale * z + c

Here, c is the constant being tested, and scale is a real number.

Let me know what you think