Fractal transformations of recursive walks in the Julia fern

One of the most studied fractals corresponds to the Julia Set and one of its elements can be obtained with the following recursive formula in the complex plane: Zi+1 = Zi2 - 1, the result depends on the chosen starting complex number. We can define the Julia set of a complex variable polynomial as the boundary of the set of points that escape to infinity when iterating this polynomial. This means that the orbit of an element of the Julia set does not escape infinity.