This is a collection of programs to create and analyze trails of random walk (in 1D or 3D, optionally with bias and/or bounds), presented as a time series. The analysis is done by estimating the fractal dimension of the trails and yields the timescales of correlations as well as their strength.

I used the techniques for creating and analyzing random walk trails in a paper that is available in the doc/ directory. This paper has the formulae for estimating the fractal dimension. The code in this repository is a clean-up/rewrite of the code used for that paper.

There is also a little code, called mandelbrot_cartoons.py, to create some fractal trails that Mandelbrot calls cartoons (see, e.g., Chapter 1 in "Multifractals and 1/f Noise: Wild Self-affinity in Physics." New York NY: Springer, 1999). This is a work in progress, but already has some material to build various generalizations of Brownian motion.

trail_maker.py uses NumPy and argparse.

trail_analyzer uses NumPy, argparse, Cython and GSL. To use it, first create trail_length_calc.so by running

python setup.py build_ext --inplace

mandelbrot_cartoons.py uses NumPy, SciPy optimization routines, argparse and PyX

Keywords: Fractals -- fractal dimension -- Brownian motion -- random walk

Atakan Gürkan [email protected]