The Julia set
The Julia set is a fractal. It can be rendered by, for each point $(x,y)$ in a grid (ideally centered around $(0,0)$), taking the complex number $z = x + iy$ and applying $f_c(z) = z^2 + c$ to it repeatedly until it escapes some threshold from the origin. The precise values used are variable and somewhat open to artistic interpretation; in the code below, we use $c = -0.8 + 0.156i$ and a threshold of $1.9$.
Here is a gif of the lower-right-hand-quadrant of the Julia set where each frame has one more iteration of $f_c(z)$ than the previous one.
And here is the code which produces it: