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Also: quick-and-dirty 2D Lyapunov in the Terminal window:

Multi-dimensional Lyapunov Fractals

This code accompanies the article Exploring Lyapunov Space.

As the article explains, I worked on this code initially in 2011, managing to produce some interesting results. However, I got stuck in the mire of OpenGL and OpenCL support in OS X and Linux, rather than working on the algorithm itself -- the interesting bit.

As of March 2018, I've started playing with it again, clearing it up, and converting from OpenCL to CUDA, and with the aim of getting it working well on a Jetson TX2 to allow more experimentation.

I think my goal should be to separate the calculation code completely into a networked worker, and an entirely separate GUI client that just consumes data produced by the worker(s); perhaps with a central manager node to mediate between the two. Perhaps things like MPI would be a good way to do this.


This code monopolises the primary GPU, so your computer may become completely unresponsive, even once the program has quit. Yes, even if you SSH in and kill the program. So, make sure you have saved all work and shut down all other apps to minimise the damage of a hard reboot.

Also, this code is basically seven years old (at the time of writing) and horribly unfinished and hacky. In particular, the offline code is particularly ropey, as I stopped updating it once I'd started on the interactive version.


This code did once work on an Ubuntu Linux machine, but hasn't been tested since. It does seem to work (to some extent) on my 2016 MacBook running macOS Sierra with only tiny tweaks, which is a minor miracle.

To install on macOS, make sure you have Homebrew installed and do:

	brew install libpng glew

to install the glew OpenGL library used by the interactive app, and the png library used by the offline programs.


    make lyap_interactive && ./lyap_interactive

and hope for the best. I do not accept responsibility for data loss and/or damage caused by this code.

Please don't judge me for the poor quality of code. It really doesn't live up to my personal quality standards -- especially w.r.t. commenting -- which is something I'm really regretting as I pick it up six years later.


Hmm. I suppose it's GPLv3 really. I usually prefer Apache or similar for my code, but being somewhat of a passion of mine over many years and of purely academic interest, this work is something I wouldn't mind some attribution on.

I really do encourage interested parties to help tidy it up and take it forward, though. I just don't want to be lost in the kerfuffle.

So unless you arrange with me in advance for it to be licensed differently, the code is Copyright 2011-2018, Tom Gidden and available under the terms of the GNU Public License version 3.


Lyapunov fractals extended into the third (and fourth) dimension








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