The Mandelbrot set, named after Benoît Mandelbrot, led to a broad range of research as well as inspiring and appealing results. Even though there is no analogue description in 3-space, several extensions were considered. In this article, we recall the spherical representation and discuss a possible reformulation of trigonometric functions to improve the rendering performance. Afterwards, we set up a multiplication in 3-space, motivated by the cross product and its relation to differential forms. These provide the possibility to choose two functions as coefficients to achieve a varying multiplication in space, which we experimentally investigate using two iteration schemes and several function pairs. Finally, we turn to Julia sets, which can be achieved due to a minor change in the usual Mandelbrot iteration scheme and we explore examples w.r.t. function and constant choices.