Research

Strange Attractor project

My original applet (well first there was a C program… but it's not released anywhere). http://pix.test.at/java/lung

This is a silly song about the Mandelbrot Set, but it reminded me that my plans to map out the number space occupied by stange attractors are similar to the method for calculating this kind of fractal. Only the equation for the Mandelbrot Set is simpler (but the simplicity is most of the reason it is interesting). The similarity is that commonly seen plots of the Mandelbrot set are a visualisation of the trend of the results of the iterative equations (what I intend to map), rather than the results themselves (what I am currently visualising). http://www.youtube.com/watch?v=lIlwFpz9s_I

Here are some applets that demonstrate what is happening at successive iterations of the logistic map (and some other 1-dimensional maps). This is interesting because the attractors I am interested in are a superset of this attractor (higher order polynomial equations, and higher dimension). I wonder if it is possible to contrive a similar demonstration for higher dimensions. http://ibiblio.org/e-notes/MSet/Logistic.htm

Fyre is a program quite similar to the navigator I would like to make, although only 2D, and working with a different function. Their program explores the De Jong map according to this page