The complexity of sequences generated by the arc-fractal system
Huynh, Hoai Nguyen
Chew, Lock Yue
Date of Issue2015
School of Physical and Mathematical Sciences
We study properties of the symbolic sequences extracted from the fractals generated by the arc-fractal system introduced earlier by Huynh and Chew. The sequences consist of only a few symbols yet possess several nontrivial properties. First using an operator approach, we show that the sequences are not periodic, even though they are constructed from very simple rules. Second by employing the ϵ-machine approach developed by Crutchfield and Young, we measure the complexity and randomness of the sequences and show that they are indeed complex, i.e. neither periodic nor random, with the value of complexity measure being significant as compared to the known example of logistic map at the edge of chaos. The complexity and randomness of the sequences are then discussed in relation with the properties of associated fractal objects, such as their fractal dimension, symmetry and orientations of the arcs.
DRNTU::Science::Chemistry::Physical chemistry::Molecular structure and bonding
© 2015 Huynh et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.