Julia set is a set of complex numbers that is studied in the field of complex dynamics.

It is defined by a function \(f(z) = Z^2 + C\) of complex domain, where \(Z\) is current point in the plane and \(C\) is a hyper parameter that changes the behaviour of the system.

We compute the set by testing for every point on a plane if that point \(Z\) "*converges*" towards some
other point (in other words it remains "bounded") or "*diverges*" towards
infinity after \(n\) iterations. Points that remain bounded are part of the Julia set.

\(C = 0.0 + 0.0i\)

\(C = -0.61 + 0.0i\)

\(C = 0.33 + 0.0i\)

\(C = 0.33 + 0.5i\)

\(C = 0.61 + 0.52i\)

\(C = 0.35 + 0.04i\)

\(C = 0.44 + 0.34i\)

\(C = -0.65 + 0.04i\)

\(C = -0.65 + 0.04i\)