We’ll continue the theme of this fledgling blog along the lines of fractals, pretty pictures, spirals and Matlab. All of this neatly encapsulated in the concept of the damped and driven oscillator, alluded to somewhat scandalously in the title. In particular, for simplest conceptualisation (and maximum innuendo potential) we’ll look at the humble pendulum.
I was told an example interview question involving ants following one another around in a square, and it continued to bug me for a while (pun wholeheartedly intended). The specific wording of the problem is this:
4 ants are place at the corners of a square of unit area, and each ant walks towards the ant ahead of it. What is the shape of the path the ants take, and how far do they walk until they meet?
Sounds fun and relatively simple (though not so much in an interview situation!), lets have a look.
When initially fiddling around and getting to grips with Matlab a while ago, I had a go at implementing the ‘logistic map’, a well known mathematical process which leads to deterministic chaos.
To simulate your own WiFi signal, check out:
I’ve recently moved into a new flat, and to celebrate I bought a WiFi card for my PC rather than relying on a power line LAN adaptor – plug sockets are a valuable resource in a Victorian flat conversion and so shouldn’t be wasted on such trivial things.
Unfortunately, with my lovely new card freshly installed my connection was erratic at best, disconnecting more or less at random and generally being a first-class first-world problem. In a fit of internet-deprived mania I decided to investigate, the first act being to crash out a quick CAD drawing of the flat layout in Sketchup:
The above image is of a few iterations of a Newton fractal.
Assuming that isn’t quite enough information for you, a Newton fractal is a 2D plot of the complex plane – that is to say real numbers along the horizontal axis and imaginary along the vertical – where each point is coloured by the value of a complex number there.
Almost looks like work 