Discrete dynamical systems

You can find an introduction to k-automata here. It is a revised version of a presentation I once gave.

An implementation of k-automata including examples written in C. Non-k-automata can also be constructed, the Fibonacci automaton is included as an example. The class of automata this program accepts is described in this document about Numeration-automatic sequences. Note that you do not need to feed an arbitrary automaton with the correct expansion, you could filter out all the 'garbage'.

A simple implementation of substitutions in general used to verify the correctness of the constructed automata.

An online version of the program is also available and here is the source for those who want to run this program on their own webserver.

The source is also available via git:

git clone git://fixedpoint.nl/numauto

Related to this work, I have contributed to the On-Line Encyclopedia of Integer Sequences.

The Fibonacci sequence: A000045.

Other sequences: A101399, A101400, A101169, A101197, A101168.