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… read more

Submitted on 22 May 2018

Turtle Graphics in Python

Figure 1. First four stages of the Koch snowflake.

Turtle graphics are a way of drawing where you control a cursor, known as the “turtle”, by instructing it how to move. For example, you tell the turtle to move forward over a certain distance, drawing a line on your screen in the process, then… read more


Submitted on 7 May 2018

How to Create Animated GIFs with Python

Animated Mandelbrot fractal

To close the series of articles on how to compute fractals using NumPy array operations, I want to show you one more thing: how to create animated GIFs from those NumPy arrays. The first point to make is that… read more


Submitted on 9 April 2018

Exponentiation by Squaring

In this article, I present the simple idea of exponentiation by squaring. This idea saves computation time in determining the value of large integer powers by “splitting” the exponentiation in a clever way into a series of squaring operations. The technique is based on the fact that… read more

Submitted on 12 February 2017

Mandelbrot Set

Detail of the Mandelbrot set

The Mandelbrot set is named after Benoît Mandelbrot, a French American mathematician. The set is a part of the complex plane. It is created by iterating the complex quadratic polynomial \(f_c(z)=z^2+c\). For each point \(c\) of the complex plane… read more

Submitted on 17 May 2012


Detail of the Mandelbrot set When I was writing an article on the Mandelbrot set, I looked for software to generate illustrations. Needless to say that there is lots of stuff available for a colorful subject like that. But, lo and behold, I discovered that the venerable Fractint still exists, and is actually still maintained! The program…


Submitted on 1 May 2012