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The complexity of sequences generated by the arc-fractal system

, : The complexity of sequences generated by the arc-fractal system. Plos One 10(2): E0117365-E0117365

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.


PMID: 25700034

DOI: 10.1371/journal.pone.0117365

Other references

Vizzotto, S.; Melsohn, I., 1959: Schizophasia. Arquivos de Neuro-Psiquiatria 17(2): 207-214

Lopes, S.I.G.; Lopes, M.S.; Oliveira, M.A.B.; Mattioli Filho, G.; Horowitz, N., 1993: Rates and dates of application of potassium to irrigated rice. In field experiments at Cachoeira, Brazil, response of the rice cultivar BR-IRGA 409 to potassium fertilizer was small in the first year (0.69 t/ha over the control) but increased in the following year to 1.40 t/ha more than the control. Best resu...

Worrall, G.A., 1961: Work on improvement of saline-alkali land on the University Farm, Khartoum, 1956-59. Over the 3 years of the experiment the salt in the top 2 ft. of the soil was reduced by almost 1/2 of the original amount, and nearly all this was removed in the 1st season. The movement was downwards, and there was little evidence of any upward m...

Alkema, H.D.; Ratliff, R.K., 1967: Successful treatment of post-radiation ureteral stricture by simple linear incision. Journal of Urology 97(2): 251-253

Paepke, Hans-Joachim., 1993: Uber nordliche Vorkommen von Macropodus ocellatus. DATZ. Januar; 461: 50-52

Haendel, M.A.; Vasilevsky, N.; Brush, M.; Hochheiser, H.S.; Jacobsen, J.; Oellrich, A.; Mungall, C.J.; Washington, N.; Köhler, S.; Lewis, S.E.; Robinson, P.N.; Smedley, D., 2016: Disease insights through cross-species phenotype comparisons. New sequencing technologies have ushered in a new era for diagnosis and discovery of new causative mutations for rare diseases. However, the sheer numbers of candidate variants that require interpretation in an exome or genomic analysis are still...

Zabalov, M.V.; Karlov, S.S.; Lemenovskii, D.A.; Zaitseva, G.S., 2005: A DFT investigation of alkyne bromination reactions. [Structure: see text]. A DFT calculation study of the addition reaction between molecular bromine and the number of symmetrical or unsymmetrical substituted alkynes 1 (R-CC-R'), where R = R' = H (1a), Me (1b), t-Bu (1c), or Ph (1d), or R...

Dodd N.J.F., 1990: Food irradiation and free radicals. Analytical Proceedings 27(8): 227

Sopnev, A.V.; Nagornov, M.N., 2003: Different aspects of application of digital photography in forensic medicine. Sudebno-Meditsinskaia Ekspertiza 46(4): 42-45

King, V.; Terenghi, G.; Brown, R.; Priestley, J.V., 1998: Fibre ingrowth into neurotrophin impregnated fibronectin mats implanted into the damaged rat spinal cord. Society for Neuroscience Abstracts 24(1-2): 37