A blog of Python-related topics and code.
Superellipses
Posted by: christian on 3 Nov 2017
A superellipse (also called a Lamé curve) is the curve described by the equation $$ \left|\frac{x}{a}\right|^p + \left|\frac{y}{b}\right|^p = 1 $$ For $n=2$, this is the equation of an ordinary ellipse and for $a=b=1$ that ellipse is a circle. The corresponding curve for $p=4$ is sometimes called a squircle.
Cobweb plots
Posted by: christian on 1 Nov 2017
A cobweb plot is often used to visulaize the behaviour of an iterated function. That is, the sequence of values obtained from setting $x_{n+1} = f(x_n)$, starting at some value $x_0$.
Evolution of a free particle
Posted by: christian on 28 Oct 2017
This post is based on Problem 2.22 from Griffiths, Introduction to Quantum Mechanics (Prentice Hall, 1995).
Simulating the Belousov-Zhabotinsky reaction
Posted by: christian on 27 Jul 2017
The Belousov-Zhabotinsky (BZ) reaction is a classical example of a non-equibrium chemical oscillator in which the components exhibit periodic changes in concentration.
The harmonically-driven pendulum
Posted by: christian on 25 Jul 2017
For the purposes of this article, the harmonically-driven pendulum is one whose anchor point moves in time according to $x_0(t) = A\cos\omega t$. As with previous posts, the position of the pendulum bob with time can be described using Lagrangian mechanics. In a coordinate system with the pendulum anchor initially at $(0,0)$ and the $y$-axis pointing up, the components of the bob position and velocity as a function of time are: