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…
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…
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…
If you use NumPy for numerical computations, which I recommend if you program in Python, one of the key things to do is to process entire arrays in one go as much as possible (this is also true for MATLAB). Using these so-called vectorized operations makes sure that…
Do you know what a quine is? Here is an example in Python…
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…
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…
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…