Summary
Complex-dynamical fractal is a hierarchy of permanently, chaotically changing versions of system structure, obtained as the unreduced, causally probabilistic general solution to an arbitrary interaction problem. Intrinsic creativity of this extension of usual fractality determines its exponentially high operation efficiency, which underlies many specific functions of living systems, such as autonomous adaptability, “purposeful” development, intelligence and consciousness (at higher complexity levels). We outline in more detail genetic applications of complex-dynamic fractality, demonstrate the dominating role of genome interactions, and show that further progressive development of genetic research, as well as other life-science applications, should be based on the dynamically fractal structure analysis of interaction processes involved. We finally summarise the obtained extension of mathematical concepts and approaches closely related to their biological applications.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Losa GA, Nonnenmacher TF, Weibel ER, eds. Fractals in Biology and Medicine. Basel: Birkhäuser, 1994.
Losa GA, Nonnenmacher TF, Merlini D, Weibel ER, eds. Fractals in Biology and Medicine, Vol. II. Basel: Birkhäuser, 1998.
Losa GA, Merlini D, Nonnenmacher TF, Weibel ER, eds. Fractals in Biology and Medicine, Vol. III. Basel: Birkhäuser, 2002.
Mandelbrot B. The Fractal Geometry of Nature. San Francisco: Freeman, 1982.
Mandelbrot B. Fractales, hasard et finance, 1959–1997. Paris: Flammarion, 1998.
Feder J. Fractals. New York: Plenum Press, 1988.
Peintgen H-O, Jürgens H, Saupe D. Chaos and Fractals. New Frontiers of Science. New York: Springer-Verlag, 1992.
Nakayama T, Yakubo K, Orbach RL. Dynamical properties of fractal networks: scaling, numerical simulations, and physical realisations. Rev Mod Phys 1994; 66: 381–443.
Kirilyuk AP. Universal Concept of Complexity by the Dynamic Redundance Paradigm: Causal Randomness, Complete Wave Mechanics, and the Ultimate Unification of Knowledge. Kiev: Naukova Dumka, 1997. For a non-technical review see also: e-print physics/9806002 at http://arXiv.org.
Kirilyuk AP. The universal dynamic complexity as extended dynamic fractality: causally complete understanding of living systems emergence and operation. In: Losa GA, Merlini D, Nonnenmacher TF, Weibel ER, eds. Fractals in Biology and Medicine, Vol. III. Basel: Birkhäuser, 2002; 271–84. E-print physics/0305119.
Kirilyuk AP. Dynamically Multivalued, Not Unitary or Stochastic, Operation of Real Quantum, Classical and Hybrid Micro-Machines. E-print physics/0211071 at http://arXiv.org.
Kirilyuk AP. Universal symmetry of complexity and its manifestations at different levels of world dynamics. Proceedings of Institute of Mathematics of NAS of Ukraine 2004; 50: 821–8. E-print physics/0404006 at http://arXiv.org.
Kirilyuk AP. Dynamically multivalued self-organisation and probabilistic structure formation processes. Solid State Phenomena 2004; 97–8: 21-6. E-print physics/0405063 at http://arXiv.org.
Kirilyuk AP. Theory of charged particle scattering in crystals by the generalised optical potential method. Nucl Instr Meth B 1992; 69: 200–231.
Kirilyuk AP. Quantum chaos and fundamental multivaluedness of dynamical functions. Annales de la Fondation Louis de Broglie 1996; 21: 455–480. E-prints quant-ph/9511034-36 at http://arXiv.org.
Dederichs PH. Dynamical diffraction theory by optical potential methods. In: Ehrenreich H, Seitz F, Turnbull D, eds. Solid State Physics, Vol. 27._New York: Academic Press, 1972; 136–237.
Taft RG, Mattick JS. Increasing biological complexity is positively correlated with the relative genome-wide expansion of non-protein-coding DNA sequences. Eprint q-bio.GN/0401020 at http://arXiv.org.
Horgan J. The End of Science. Facing the Limits of Knowledge in the Twilight of the Scientific Age. Helix: Addison-Wesley, 1996.
Kline M. Mathematics: The Loss of Certainty. New York: Oxford University Press, 1980.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Birkhäuser Verlag Basel
About this paper
Cite this paper
Kirilyuk, A. (2005). Complex-Dynamical Extension of the Fractal Paradigm and its Applications in Life Sciences. In: Losa, G.A., Merlini, D., Nonnenmacher, T.F., Weibel, E.R. (eds) Fractals in Biology and Medicine. Mathematics and Biosciences in Interaction. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7412-8_23
Download citation
DOI: https://doi.org/10.1007/3-7643-7412-8_23
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7172-2
Online ISBN: 978-3-7643-7412-9
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)