Scaling in nature: From DNA through heartbeats to weather

S. Havlin, S. V. Buldyrev, A. Bunde, A. L. Goldberger, P. Ch Ivanov, C. K. Peng, H. E. Stanley

Research output: Contribution to journalConference articlepeer-review

79 Scopus citations


The purpose of this report is to describe some recent progress in applying scaling concepts to various systems in nature. We review several systems characterized by scaling laws such as DNA sequences, heartbeat rates and weather variations. We discuss the finding that the exponent α quantifying the scaling in DNA in smaller for coding than for noncoding sequences. We also discuss the application of fractal scaling analysis to the dynamics of heartbeat regulation, and report the recent finding that the scaling exponent α is smaller during sleep periods compared to wake periods. We also discuss the recent findings that suggest a universal scaling exponent characterizing the weather fluctuations.

Original languageEnglish
Pages (from-to)46-69
Number of pages24
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1-2
StatePublished - 1 Nov 1999
EventProceedings of the 1999 13th Max Born Symposium on 'Statistical Physics in Biology: Perspectives in DNA Analysis, Population Dynamics and Ageing' - Wroclaw, Poland
Duration: 26 May 199930 May 1999

Bibliographical note

Funding Information:
We are grateful to many individuals, including R. Mantegna, F. Sciortino, M. Simons, M.G. Rosenblum, J. Fritsch-Yelle, R.M. Baevsky, L.A.N. Amaral, J. Mietus, E. Koscielny-Bunde, H.E. Roman, Y. Goldreich, H.J. Schellnhuber for major contributions to the results reviewed here which represent collaborative research efforts. We also wish to thank M. Azbel, C. Cantor, C. DeLisi, M. Frank-Kamenetskii, A. Yu. Grosberg, G. Huber, I. Labat, L. Liebovitch, G.S. Michaels, P. Munson, R. Nossal, R. Nussinov, R.D. Rosenberg, J.J. Schwartz, M. Schwartz, E.I. Shakhnovich, M.F. Shlesinger, N. Shworak, and E.N. Trifonov for valuable discussions. Partial support was provided by the National Science Foundation, National Institutes of Health (Human Genome Project), the G. Harold and Leila Y. Mathers Charitable Foundation, the National Heart, Lung and Blood Institute, the National Aeronautics and Space Administration (NASA), the Israel-USA Binational Science Foundation, and the Israel Academy of Sciences.


  • DNA
  • Fractals
  • Heartbeat
  • Scaling
  • Time series
  • Weather


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