Aleph Zero Home

Interactive computer mathematics

Driven Pendulum Simulation.

Here you can explore the various behaviours exibited by a pendulum that is subject to a driving force.

This simulation was inspired by "Chaotic Dynamics, an introduction" by G.L.Baker and J.P.Gollub. The simulation uses javascript and requires HTML5.
Volterra-Lotka Fractal.

By changing the parameters, you can find a number of different "strange attractors" including one which has the form of a wiggly loop.

The fractal explorer is based on a description given by Peitgen and Richter in their book "The Beauty of Fractals"
Iterated Function Systems.

Here you can view some standard examples, or enter your own coefficients.

In his book "Fractals, a very short introduction", Kenneth Falconer describes how to draw the fractal defined by an iterated function system (IFS). This method was introduced by Michael Barnsley, and is a kind of random walk.
Loxodromic paths.
Loxodromic paths are mentioned in "Indra's Pearls" by Mumford, Series and Wright. The word "loxodromic" was new to me, so here is a little exploration.