Mandelbox

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.

[1] It is typically drawn in three dimensions for illustrative purposes.

[2][3] The simple definition of the mandelbox is this: repeatedly transform a vector z, according to the following rules: The iteration applies to vector z as follows:[clarification needed] Here, c is the constant being tested, and scale is a real number.

[3] A notable property of the mandelbox, particularly for scale −1.5, is that it contains approximations of many well known fractals within it.

the mandelbox sides have length 4 and for