Complex-Dynamical Extension of the Fractal Paradigm and Its Applications in Life Sciences

Kirilyuk, Andrei (2004) Complex-Dynamical Extension of the Fractal Paradigm and Its Applications in Life Sciences. [Conference Paper] (In Press)


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Complex-dynamical fractal is a hierarchy of permanently, chaotically changing versions of system structure, obtained as the unreduced, causally probabilistic general solution of arbitrary interaction problem (physics/0305119, physics/9806002). 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. The obtained complex-dynamical fractal of a living organism specifies the intrinsic unification of its interaction dynamics at all levels, from genome structure to higher brain functions. We finally summarise the obtained extension of mathematical concepts and approaches closely related to their biological applications.

Item Type:Conference Paper
Additional Information:12 pages, 24 eqs, 19 refs; Report presented at the IVth International Symposium "Fractals in Biology and Medicine" (Ascona, 10-14 March 2004),
Keywords:Dynamic multivaluedness; entanglement; complexity; chaos; probabilistic fractal; living fractal; genomics; constructive genetics; genome interaction; genetic bomb; integral medicine; biofractal; biomathematics
Subjects:Computer Science > Complexity Theory
Computer Science > Artificial Intelligence
Biology > Theoretical Biology
ID Code:4140
Deposited By:Kirilyuk, Andrei
Deposited On:27 Mar 2005
Last Modified:11 Mar 2011 08:55

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[1] Losa GA, Nonnenmacher TF, Weibel ER, eds. Fractals in Biology and Medicine. Basel: Birkhäuser, 1994.

[2] Losa GA, Nonnenmacher TF, Merlini D, Weibel ER, eds. Fractals in Biology and Medicine, Vol. II. Basel: Birkhäuser, 1998.

[3] Losa GA, Merlini D, Nonnenmacher TF, Weibel ER, eds. Fractals in Biology and Medicine, Vol. III. Basel: Birkhäuser, 2002.

[4] Mandelbrot B. The Fractal Geometry of Nature. San Francisco: Freeman, 1982.

[5] Mandelbrot B. Fractales, hasard et finance, 1959-1997. Paris: Flammarion, 1998.

[6] Feder J. Fractals. New York: Plenum Press, 1988.

[7] Peintgen H-O, Jürgens H, Saupe D. Chaos and Fractals. New Frontiers of Science. New York: Springer-Verlag, 1992.

[8] Nakayama T, Yakubo K, Orbach RL. Dynamical properties of fractal networks: scaling, numerical simulations, and physical realisations. Rev Mod Phys 1994; 66: 381-443.

[9] 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

[10] 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.

[11] Kirilyuk AP. Dynamically Multivalued, Not Unitary or Stochastic, Operation of Real Quantum, Classical and Hybrid Micro-Machines. E-print physics/0211071 at[12] 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 .

[13] Kirilyuk AP. Dynamically multivalued self-organisation and probabilistic structure formation processes. Solid State Phenomena 2004; 97-8: 21-6. E-print physics/0405063 at

[14] Kirilyuk AP. Theory of charged particle scattering in crystals by the generalised optical potential method. Nucl Instr Meth B 1992; 69: 200-231.

[15] 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

[16] 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.

[17] Taft RG, Mattick JS. Increasing biological complexity is positively correlated with the relative genome-wide expansion of non-protein-coding DNA sequences. E-print q-bio.GN/0401020 at

[18] Horgan J. The End of Science. Facing the Limits of Knowledge in the Twilight of the Scientific Age. Helix: Addison-Wesley, 1996.

[19] Kline M. Mathematics: The Loss of Certainty. New York: Oxford University Press, 1980.


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