The Mandelbulb Graphical Pattern

The Mandelbulb is a three-dimensional fractal, constructed by Daniel White and Paul Nylander using spherical coordinates in 2009.[1] A canonical 3-dimensional Mandelbrot set does not exist, since there is no 3-dimensional analogue of the 2-dimensional space of complex numbers. It is possible to construct Mandelbrot sets in 4 dimensions using quaternions and bicomplex numbers. White and Nylander's formula for the "nth power" of the vector v=⟨x,y,z⟩ in ℝ3 is vn:=rn⟨sin⁡(nθ)cos⁡(nϕ),sin⁡(nθ)sin⁡(nϕ),cos⁡(nθ)⟩ wherer=x2+y2+z2,ϕ=arctan⁡(y/x)=arg⁡(x+yi), andθ=arctan⁡(x2+y2/z)=arccos⁡(z/r).

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Atacac micro factory

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