Fractals: The beautiful complex patterns generated by simple iterative computations: Some examples
A hierarchy of selfsimilar structures: The large scale is a magnified version of the small scale.
Numerical computations such as addition,multiplication,etc.,have inherent round-off errors. Iterative computations magnify this round-off error because of feedback with amplification. The round-off error growth structures generate the beautiful fractal patterns.
The complex structures found in nature are all fractals,i.e.,posses selfsimilar geometry. Simple iterative growth processes may underlie the complex patterns found in nature
The most fundamental selfsimilar structure is the forking (bifurcating) structure (Jean, 1994 References) of tree branches, tree roots, river tributaries, branched lightning, etc. The hierarchy of complex branching structures occupy only a part (fraction) of 3-dimensional space or a fraction of 2-dimensional space in a 2-dimensional projection, and therefore they belong to the recently identified (Mandelbrot, 1977) category of fractal objects. The study of fractals now belongs to the new field nonlinear dynamics and chaos, a multidisciplinary area of intensive research in all fields of science in recent years. Golden mean and selfsimilar, fractal geometrical structures in nature
Numerical integration schemes incorporate iterative computations.Propagation of round-off error into the main stream
computation results in deterministic chaos in computer realizations of nonlinear mathematical models used for simulation of real
world dynamical systems.
Selfsimilar spatial structures imply long-range spatial correlations or non-local connections.
Global cloud cover pattern exhibits fractal geometry.The existence of long-range spatial correlations such as the El-Nino impact
on global climate is now accepted.The global atmosphere acts as a unified whole, where,local perturbations produce a global
response.
Long-range spatiotemporal correlations (non-local connections) in atmospheric flows
A superstring theory for atmospheric flow dynamics?
Cantorian Fractal Spacetime, Quantum-like Chaos and Scale Relativity in Atmospheric Flows by A.M.Selvam and Suvarna Fadnavis Published with modification in Chaos,Solitons and Fractals( vol 10(9), 1577-1582, 1999)
The unmodified paper(html) is available at eprint archives http://xxx.lanl.gov/abs/chao-dyn/9808015
A cell dynamical system model for thundercloud electrification by A.M.Selvam Proc. 1988 Int'l Conf. Lightning and Static Electricity, 26-28 September 1989, University of Bath, U.K.
The paper(html) is available at eprint archives http://xxx.lanl.gov/abs/chao-dyn/9809002
Cantorian Fractal Spacetime and Quantum-like Chaos in Neural Networks of the Human Brain by A.M.Selvam Published with
modifications in CHAOS,SOLITONS AND FRACTALS ( vol 10(1), 25-29, 1999)
The unmodified paper(html) is available at eprint archives http://xxx.lanl.gov/abs/chao-dyn/9809003
Possible Solar Influence on Atmospheric Electric Field by Poonam Sikka, A.Mary Selvam and A.S.Ramachandramurty Preprint volume : VII International Conference on Atmospheric Electricity, June 3-8, 1984, Albany, N. Y. American Meteorological Society, Boston, Mass., USA
The paper(html) is available at eprint archives http://xxx.lanl.gov/abs/chao-dyn/9806014
A study of circadian rhythm and meteorological factors influencing acute myocardial infarction by A.M.Selvam, D.Sen, S.M.S. Mody Research Report No. RR-073, Indian Institute of Tropical Meteorology, Pune 411 008, India, April 1997
The paper(html) is available at eprint archives http://xxx.lanl.gov/abs/chao-dyn/9812014
REVIEW OF WARM CLOUD MODIFICATION by A.S.R.MURTY World Meteorological Organization, WMP Report No. 24, WMO/TD-No. 687
Eighteenth Session of the Executive Council Panel of Experts/CAS Working Group on Physics and Chemistry of Clouds and Weather Modification Research
Geneva, Switzerland, 30 January – 3 February 1995
Appendix D, pp.1-5.
WARM CLOUD MODIFICATION: A VIEWPOINT by A.S.R.MURTY World Meteorological Organization, WMP Report No. 27, WMO/TD-No. 820
Eighteenth Session of the Executive Council Panel of Experts/CAS Working Group on Physics and Chemistry of Clouds and Weather Modification Research
Geneva, Switzerland, 5 – 9 May 1997
Appendix D, pp.31-33.
Some thermodynamical and microphysical aspects of monsoon clouds.
A. Mary Selvam, A. S. Ramachandra Murty, R. Vijayakumar, S. K. Paul, G. K. Manohar, R. S. Reddy, B. K. Mukherjee and Bh. V. Ramana Murty
Proceedings of the Indian Academy of Sciences, 1980, 87(A), 2 July, 1980, 215-230.
Simulation of Urban Effects of Cloud Physical Parameters by A.Mary Selvam and A.S.R.Murty
Proc. International Conference on Energy Transformations and Interactions with Small and Meso-scale Atmospheric Processes, 2-6 March 1987, Switzerland
The paper(html) is available at eprint archives
http://xxx.lanl.gov/html/physics/0006031
Deterministic chaos, fractals, and quantumlike mechanics in atmospheric flows
(HTML) by A.Mary Selvam
Canadian J. Phys. 68, 831 - 841 (1990)
The paper(html) is available at eprint archives
http://xxx.lanl.gov/html/physics/0010046
Nonlinear Dynamics and Chaos: Applications for Prediction of Weather and Climate by
J.S.Pethkar and A.M.Selvam
Proc. TROPMET 97, Bangalore, India, 10-14 Feb. 1997.
The paper(html) is available at eprint archives
http://xxx.lanl.gov/html/physics/0104056
Universal Spectrum for Natural Variability of Climate : Implications for Climate Change by
J.S.Pethkar and A.M.Selvam
Amer. Meteorol. Soc.10th Conf. Applied Climatology, Fall 1997, Western USA.
The paper(html) is available at eprint archives
http://xxx.lanl.gov/html/physics/0105109
Quantumlike Chaos in the Frequency Distributions of the Bases A, C, G, T in human chromosome 1 DNA. by A.M.Selvam http://arxiv.org/html/physics/0211066
Proceedings of 2nd WSEAS Int. Conf. on NON-LINEAR ANALYSIS, NON-LINEAR SYSTEMS AND CHAOS(NOLASC 2003)
WSEAS MMACTEE-WAMUS-NOLASC 2003, Vouliagmeni, Athens, Greece, December 29-31, 2003, http://www.wseas.org
Published in the Canadian electronic journal APEIRON, Volume 11 Number 3 (July 2004), 134-146. http://redshift.vif.com/JournalFiles/V11NO3PDF/V11N3SEL.PDF
Deterministic Chaos: A signature of Quantumlike Mechanics in Self-Organized Adaptive Networks by A.M.Selvam Proc. IEEE, NAECON 91, Dayton, U. S. A. May 20-24, 1991 http://arxiv.org/html/physics/0305104
Deterministic Chaos Model for Self-Organized Adaptive Networks in Atmospheric Flows by A.Mary Selvam Proceedings of the IEEE National Aerospace and Electronics Conference - NAECON 1989, Dayton, OH, May 22-26, 1989, 1145-1152. http://arxiv.org/html/physics/0308094
The Dynamics of Deterministic Chaos in Numerical Weather Prediction Models by A.Mary Selvam Proc. American Meteorological Society 8th Conf. Numerical Weather Prediction, February 1988, Baltimore, MD., USA.
Identification of self-organized criticality in atmospheric low frequency variability by R. R. Joshi and A. M. Selvam
published in Fractals, Vol. 7, No. 4 (1999) 421-425
A General Systems Theory for the Observed Fractal Space-Time Fluctuations in Dynamical Systems by A. M. Selvam http://arxiv.org/pdf/physics/0404014
Fractal space-time fluctuations: A signature of quantumlike chaos in dynamical systems by A. M. Selvam
Also available at http://arxiv.org/pdf/physics/0408089
International Journal of Physics, Vol. 3, No. 1, January-June 2010 pp. 57-65
Signatures of a universal spectrum for nonlinear variability in daily columnar total ozone content. Adv. Atmos. Sci. 11(3), 335-342, 1994 by A.
M.Selvam and M. Radhamani
The pages 335 to 342 are available at aasp8.pdf
Identification of self-organized criticality in atmospheric total ozone variability. Proc. Int'l. Symp. Middle Atmospheric Sciences, (MAS Symposium), Kyoto, Japan, 23-27 March. 1992 by A.
M.Selvam and M. Radhamani
The pages 76 to 77 are available at mas2p.pdf
Trends in Continuum Physics, TRECOP ’98; Proceedings of the International Symposium on Trends in Continuum Physics, Poznan, Poland, August 17-20, 1998. Edited by Bogdan T. Maruszewski, Wolfgang Muschik, and Andrzej Radowicz. Singapore, World Scientific, 1999, 334(12).