Mandelbox

The Mandelbox is an escape-time fractal introduced by Tom Lowe in 2010. For a vector , define the box fold componentwise by

(1)

Thus the box fold reflects each coordinate lying outside the hypercube across the nearest face of the hypercube. For , define the ball fold by

(2)

where is the Euclidean norm. Given parameters and , start with and apply the iteration

(3)

The Mandelbox is the set of parameters for which the resulting map orbit is bounded. The standard Mandelbox uses , , and . The construction works in any finite dimension, although the three-dimensional Mandelbox is most commonly rendered (Helt 2018, Lowe 2021).