This fractal is non-holomorphic which makes it kind of a dumpster fire..or a burning ship I guess... The easiest layman's definition of holomorphic is any function or operations on complex numbers that doesn't peek at the real and imaginary parts of the complex number. In algebra, there is no combination of algebraic operations [1] that can do so. But on computers, we have Re(z) and Im(z), which are easy to calculate since the complex number is simply stored as two parts, and it just pulls one of them out.<p>When you violate this sacred notion, of treating a complex number as a singular entity, indivisible, the operations or functions you get, no longer have nice properties, like being analytic [2]. You are no longer doing algebra, you have gone into the realm of chaotics over R^2 with an equivalence relation through rotations, which is a far different beast.<p>That's why other fractals that treat complex numbers as first class citizens, singular entities, and don't use hacks like Re or Im, are much prettier and have less branch cuts.<p>[1] <a href="https://en.wikipedia.org/wiki/Algebraic_operation" rel="nofollow">https://en.wikipedia.org/wiki/Algebraic_operation</a><p>[2] <a href="https://en.wikipedia.org/wiki/Analytic_function" rel="nofollow">https://en.wikipedia.org/wiki/Analytic_function</a>