Fractals are mathematically calculated forms mapped on a 2D graph which, with today’s research we can map them into a 3D space (x,y,z), these formulas are algebraic and the form is achieved by infinitely repeating the same pattern at differing scales (usually smaller or self similar), these patterns can be rigid square-like grids or organic grids that look like plant growth, to many more varieties of patterns which can look arbitrary, but in fact are meticulously calculated.
However, what makes the Mandelbulb unique is its incoherent algebraic formula that makes
no mathematical sense, it does however produce a geometrically beautiful composition that is easier to translate into 3D space than other fractal formulas.
The Mandelbulb is created by continuously duplicating lengths and angles of points in space. Iterations of 4 to 8 usually produce an aesthetically pleasing Mandelbulb form.
