Complex numbers offer an orthogonal dimension to the integer number line , where multiplication aquires a rotational element. This allows intermediate 90° (π/2) multiplication and Julia's Set is shown to be a map to Madelbrot's Fractal. https://acko.net/blog/how-to-fold-a-julia-fractal/
That the Julia set and the Mandelbrot set are covariant maps on the 2D complex plane hints at the higher dimensional shape that surface Z^x + c = 0 describes.