Visualizing complex numbers and complex functions

We can colour the complex plane, so black is at the origin, white is at infinity, and the rainbow circles the origin

 

Then, a function can be plotted by putting the colour of the OUTPUT at each INPUT location

To read this: black holes are zeroes, white areas are large in absolute value, red areas are positive real, turquoise is negative real.

 

Here is a picture of the Quantum Fourier Transform matrix

The entries of the matrix are coloured as complex numbers. Change N to get bigger/smaller matrix.

 

Next two boxes: define a function and then take its QFT visually

First, in this box, define and graph a function.

 
Next, in this box, show its QFT. Rainbow colours for argument (angle), magnitude is plotted vertically.

Here’s another QFT visualizer I wrote.
 

Initialize a Complex Matrix Plotter

 

Plot the QFT with it

 

The states of two qubits, first few steps of Shor

 

An extra box