Multifractal analysis of sentence lengths in English literary texts

This paper presents analysis of 30 literary texts written in English by different authors. For each text, there were created time series representing length of sentences in words and analyzed its fractal properties using two methods of multifractal analysis: MFDFA and WTMM. Both methods showed that there are texts which can be considered multifractal in this representation but a majority of texts are not multifractal or even not fractal at all. Out of 30 books, only a few have so-correlated lengths of consecutive sentences that the analyzed signals can be interpreted as real multifractals. An interesting direction for future investigations would be identifying what are the specific features which cause certain texts to be multifractal and other to be monofractal or even not fractal at all.

[1]  Werner Ebeling,et al.  Scaling features of texts, images and time series , 2001 .

[2]  J. Kwapień,et al.  Physical approach to complex systems , 2012 .

[3]  Ludek Hrebícek.  Persistence and Other Aspects of Sentence-Length Series , 1997, J. Quant. Linguistics.

[4]  Marcel Ausloos.  Equilibrium (Zipf) and Dynamic (Grasseberg-Procaccia) method based analyses of human texts. A comparison of natural (english) and artificial (esperanto) languages , 2008, ArXiv.

[5]  K. Linkenkaer-Hansen,et al.  Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations , 2001, The Journal of Neuroscience.

[6]  H. Stanley,et al.  Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series , 2002, physics/0202070.

[7]  Ricard V. Solé,et al.  Two Regimes in the Frequency of Words and the Origins of Complex Lexicons: Zipf’s Law Revisited* , 2001, J. Quant. Linguistics.

[8]  Daniel E. Geer,et al.  Power. Law , 2012, IEEE Secur. Priv..

[9]  L. Liebovitch,et al.  "Fractal dynamics of human gait: stability of long-range correlations in stride interval fluctuations". , 1996, Journal of applied physiology.

[10]  Ricard V. Solé,et al.  Emergence of Zipf's Law in the Evolution of Communication , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Andrzej Kulig,et al.  COMPLEX NETWORK ANALYSIS OF LITERARY AND SCIENTIFIC TEXTS , 2012, 1205.4582.

[12]  Marcel Ausloos,et al.  A Comparison of natural (english) and artificial (esperanto) languages. A Multifractal method based analysis , 2008, ArXiv.

[13]  Sebastian Bernhardsson,et al.  Zipf's law unzipped , 2011, ArXiv.

[14]  J. Kwapień,et al.  Quantitative features of multifractal subtleties in time series , 2009, 0907.2866.

[15]  Werner Ebeling,et al.  Long-range correlations between letters and sentences in texts , 1995 .

[16]  S. S. Melnyk,et al.  Competition between two kinds of correlations in literary texts. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Emmanuel Bacry,et al.  THE THERMODYNAMICS OF FRACTALS REVISITED WITH WAVELETS , 1995 .

[18]  Ian H. Witten,et al.  Identifying Hierarchical Structure in Sequences: A linear-time algorithm , 1997, J. Artif. Intell. Res..

[19]  M. Newman.  Power laws, Pareto distributions and Zipf's law , 2005 .

[20]  Nicole L. Rheaume,et al.  Long-range correlation properties in motor timing are individual and task specific , 2011, Psychonomic bulletin & review.

[21]  Long-range correlations in Korean literary corpora , 2006 .

[22]  W. Ebeling,et al.  Entropy and Long-Range Correlations in Literary English , 1993, cond-mat/0204108.

[23]  J. Kwapień,et al.  Wavelet versus detrended fluctuation analysis of multifractal structures. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  M. Geyer,et al.  Long-range correlations in choice sequences of schizophrenic patients , 1999, Schizophrenia Research.

[25]  Tao Zhou,et al.  Deviation of Zipf's and Heaps' Laws in Human Languages with Limited Dictionary Sizes , 2013, Scientific reports.

[26]  C. Peng,et al.  Mosaic organization of DNA nucleotides. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[27]  Morten H. Christiansen,et al.  Language as shaped by the brain. , 2008, The Behavioral and brain sciences.

[28]  Jensen,et al.  Fractal measures and their singularities: The characterization of strange sets. , 1987, Physical review. A, General physics.