Complex Functions Visualiser

A program written in Java to visualise complex functions, using custom graphic images.

The idea behind

Let $z$ be a complex number, such that: $$z = x + iy,\ \ \ x,y \in \mathbb{R}$$ and let $f$ be any complex function: $$f: \mathbb{C} \rightarrow \mathbb{C}$$ Then, let $f(z)$ be denoted by $z'$, whereas: $$z' = x' + iy',\ \ \ x',y' \in \mathbb{R}$$
We may think of the function $f$ as a transformation in a complex plane, which moves any given point $(x,y)$ to $(x',y')$:

In this program, each pixel of a given input image will be treated as a point of coordinates $(x,y)$, and all transformed pixels will form the output image.

Program interface

Just click on the function you want to apply to the image.

Of course, you can always change the input image.
(The one chosen is relatively small: 50x50, in order for the program to work quickly.)

Example transformations

Original image

$f(z) = 10 z$

$f(z) = z^2$

$f(z) = \frac{1}{10} z^3$

$f(z) = sin(z)$

$f(z) = 200\ z^{-1}$