Animation of Julia Set using SageMath

This is an animation of a Julia set using the SageMath kernel and ffmpeg in a Jupyter-notebook environment. The function used is:

$$ f(z) = z^2 + 0.7885 e^{i \theta} $$

where $0 < \theta < 2 \pi$.

The Julia set is a fractal that arises from the iteration of a function $f(z)$ on the complex plane. The Julia set for a particular function $f(z)$ is the set of points on the complex plane that do not escape to infinity under iteration of $f(z)$.

We have plotted the Julia set for values of $a$ between $0$ and $2\pi$.