This is a program not really meant for widespread use that I've written for upcoming videos on my educational YouTube channel Guru da Ciência.
It renders .mp4 animations and .png plots of complex functions on the real and imaginary plane using Haskell, gnuplot and ffmpeg.
The x and y axis correspond to the real and imaginary components of the input; the z axis shows the magnitude of the output. The phase of the output is shown through color. Alternatively, in the files labeled with phase instead of magnitude, the third dimension stands for the complex argument of the resulting number and the fourth for the magnitude |f(z)|.
The function z^2 + c is used as an example in the included video files, where z is a complex number of the form a + bi. By calling animate $ functionList 1 (-25) 25,
the frames z^2 - 25 ... z^2 + 25 are generated and encoded into a .mp4 file.
Individual frames can be generated with plot by passing it a Haskell function, a certain step size and an interval [a,b]:
plot square 0.5 0 10 -- output.png in ./pics
By editing the gnuplot .plt files, borders, tics, title, point type, line width etc. can be specified.
Interactive versions can be found in the folder ./gnuplot-interactive which use the information contained in data.txt created by the plot method.
The pics folder needs to be empty before calling animate or plot.