Fractals, diffusion limited aggregation, and viscous fingering

The Lorentz attractor

For decades the beautiful and complex properties of fractals have continued to fascinate scientists and the public alike. Fractals have an non-integer dimension, they are self-similar, and they can be found many places in Nature. A first year project about fractals can include a mathematical description of different dimension-measures, investigation of some intuitive geometric tools like the Poincaré map, examples of strange attractors like the Lorentz attractor, and perhaps computer simulations illustrating some fractal properties of diffusion limited aggregation. It is also possible to create beautiful fractals experimentally through viscous fingering.

Suitable for: First year project

Main disciplines: Complex systems, mathematical physics, programming (any language), experiments

Related work:

Nonlinear dynamics and chaos

Diffusion-limited aggregation

Viscous fingering