What is a Voronoi Diagram?

Voronoi diagram

A Voronoi diagram is a partition of the plane into a number of cells, where each cell consists of exactly those points that are closest to the site (or seed point) of that cell. An example with ten seed points is shown in…

Tom Wed, 12/09/2020 - 19:54
There's Only One Parabola

Figure 2. Parabolas.

There is really only one circle. Of course, you have to allow for translation and scaling for this to be true, but I think you’ll agree that a large circle is essentially the same as a small one. The geometrical term for this is similarity. Two objects are similar if…

Tom Sun, 09/29/2019 - 15:46
Langton's Ant

Langton's ant

Say that you have an ant that lives on an infinite plain with tiles that can be either black or white. The ant can move in the four main directions, and it keeps moving indefinitely, according to the following two simple rules…

Tom Mon, 04/29/2019 - 09:57
Symbolic Math in Python

Yes, you can do symbolic math in Python! The library to take a look at is SymPy. This article is not a SymPy tutorial, as I only want to walk you through some examples to show you the kinds of things that it can do. A good place to start…

Tom Tue, 05/22/2018 - 20:55
How to Compute Colorful Fractals using NumPy and Matplotlib

Figure 3. Julia set for c=−0.4+0.6i, with "hot" colormap.

As a variation on the Mandelbrot fractal that I’ve computed before using NumPy array operations, I’d like to show you a few Julia fractals with some color added. I’ll concentrate on the Julia sets that are generated using the same quadratic polynomial that is used to…

Tom Sun, 03/25/2018 - 15:16
What is a Hadamard Matrix?

A Hadamard matrix is a matrix with all elements equal to \(+1\) or \(-1\), and for which the rows are mutually orthogonal. If you pick two rows from the matrix and write it as vectors \(\bf x\) and \(\bf y\), then these are orthogonal if…

Tom Wed, 12/06/2017 - 21:56

What is jerk? Jerk is to acceleration as acceleration is to velocity. And, acceleration is to velocity as velocity is to position. So let’s start there. The instantaneous velocity at which you travel tells you…

Tom Mon, 11/20/2017 - 19:34