Let's Make a Difference!
Discrete Mathematics
2009-11-06 v1 Logic in Computer Science
Abstract
We study the behaviour of iterations of the difference operator delta on streams over {0,1}. In particular, we show that a stream sigma is eventually periodic if and only if the sequence of differences sigma, delta(sigma), delta(delta(sigma)), ..., the `delta-orbit' of sigma as we call it, is eventually periodic. Moreover, we generalise this result to operations delta_d that sum modulo 2 the elements of each consecutive block of length d+1 in a given 01-stream. Some experimentation with delta-orbits of well-known streams reveals a surprising connexion between the Sierpinski stream and the Mephisto Waltz.
Cite
@article{arxiv.0911.1004,
title = {Let's Make a Difference!},
author = {Joerg Endrullis and Dimitri Hendriks and Jan Willem Klop},
journal= {arXiv preprint arXiv:0911.1004},
year = {2009}
}