Fractals

The aim of this toy-project was to experiment the features of Processing a Java-based “language for learning how to code within the context of the visual arts”. Each picture in the gallery below illustrates the dymanic of the complex map $$\begin{array}{lccc} f \colon & \mathbb C & \to & \mathbb C \newline & z & \to & z^2 + c \end{array}$$ where $c$ is a fixed complex number. The black areas correspond to the filled Julia set of $f$, i.e. the complex numbers $z$ such that the sequence $(z_n)$, defined by $z_0 = z$ and $z_{n+1} = f(z_n)$, is bounded. If $z$ does not belong to the filled Julia set, the corresponding point is colored according to the “speed” at which $(z_n)$ escape to infinity.