Physica A 300 (2001) 310–324 www.elsevier.com/locate/physa Scaling features of texts, images and time series Alexey N. Pavlov a ; ∗ , Werner Ebeling b , Lutz Molgedey b , Amir R. Ziganshin a , Vadim S. Anishchenko a a Nonlinear Dynamics Laboratory, Department of Physics, Saratov State University, Astrakhanskaya St. 83, 410026, Saratov, Russia b Institute of Physics, Humboldt-University Berlin, Invalidenstr. 110, D-10099, Berlin, Germany Received 9 January 2001 Abstract In the given paper, we consider the scaling features of long letter sequences like human writings, discretized images and discretized nancial data. Using several approaches we show that the symbolic strings and time series being analyzed have a complex multiscale structure and demonstrate dierent scalings for large and small uctuations. We discuss complex phenomena in the scaling behavior of partition functions in the case of high frequency DAX-future data. c  2001 Elsevier Science B.V. All rights reserved. PACS: 05.40.+j; 05.45.Tp; 02.50.Ey Keywords: Scaling; Multifractality; Long-range correlations; Wavelet transform 1. Introduction During the last few years there has been intense discussion about the scaling fea- tures of complex processes and natural sequences of dierent origin termed multifractal. Multiscale phenomena [1–8] occur in many elds of modern science. They take place in biosequences [9–11] and physiological signals [12,13], in fully developed turbu- lence [14–16] and random walks on random fractals [17,18], in cloud structure [19,20] and Brownian motion [21], in diusion-limited aggregates [22] and chaotic attractors [23,24], etc. Many time series in nature are nonstationary and inhomogeneous. Such signals have dierent scaling properties for dierent subsets of the data and require often a large number of characteristics to quantify the peculiarities of their complex structure [12]. * Corresponding author. Fax: +7-8452-514549. E-mail address: pavlov@chaos.ssu.runnet.ru (A.N. Pavlov). 0378-4371/01/$-see front matter c  2001 Elsevier Science B.V. All rights reserved. PII:S0378-4371(01)00341-7