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

@article{Kirilyuk2005ComplexDynamicalEO, title={Complex-Dynamical Extension of the Fractal Paradigm and Its Applications in Life Sciences *}, author={Andrei P. Kirilyuk}, journal={arXiv: General Physics}, year={2005}, pages={233-244} }

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… Expand

#### 21 Citations

Universal Science of Complexity: Consistent Understanding of Ecological, Living and Intelligent System Dynamics

- Physics, Computer Science
- 2007

Applications of universal concept of dynamic complexity are outlined emphasising cases of "truly complex" systems from higher complexity levels and show that the urgently needed progress in social and intellectual structure of civilisation inevitably involves qualitative transition to unreduced complexity understanding (the authors call it "revolution of complexity"). Expand

Complex-Dynamical Solution to Many-Body Interaction Problem and Its Applications in Fundamental Physics

- Physics
- 2012

We review the recently proposed unreduced, complex-dynamical solution to many-body problem with arbitrary interaction and its application to unified solution of fundamental problems, including… Expand

New Mathematics of Complexity and Its Biomedical Applications

- Mathematics
- 2014

We show that the unreduced, mathematically rigorous solution of the many-body problem with arbitrary interaction, avoiding any perturbative approximations and “exact” models, reveals qualitatively… Expand

Dynamic Complexity of Autonomic Communication and Software Systems

- Computer Science
- Net-Con
- 2006

The applied generalised, universally nonperturbative method of effective potential reveals the phenomenon of dynamic multivaluedness of competing system configurations forced to permanently replace each other in a dynamically random order, which leads to universally defined dynamical chaos, complexity, fractality, self-organisation, and adaptability. Expand

Dynamic Origin of Evolution and Social Transformation

- Mathematics, Physics
- 2012

We analyse the unreduced, nonperturbative dynamics of an arbitrary many-body interaction process with the help of the generalised effective potential method and reveal the well-specified universal… Expand

Unreduced Dynamic Complexity: Towards the Unified Science of Intelligent Communication Networks and Software

- Computer Science, Physics
- Net-Con
- 2005

Basic principles and first applications of the unified science of complex-dynamic communication networks and software are outlined to demonstrate its advantages and emerging practical perspectives. Expand

Unreduced Complex Dynamics of Real Computer and Control Systems

- Computer Science
- 2015 20th International Conference on Control Systems and Computer Science
- 2015

It is shown then how the obtained mathematically exact novelties of system behaviour can be applied to the development of qualitatively new, complex-dynamical kind of computer and control systems. Expand

Complex-Dynamical Approach to Cosmological Problem Solution *

- Physics
- 2005

Universe structure emerges in the unreduced, complex-dynamic interaction process with the simplest initial configuration (two attracting homogeneous fields). The unreduced interaction analysis,… Expand

Cosmological Problem Solution by Complex-Dynamical Interaction Analysis

- Physics
- 2005

Universe structure emerges in the unreduced, complex-dynamical interaction process with the simplest initial configuration (two attracting homogeneous fields). The unreduced interaction analysis… Expand

Theory of Everything, Ultimate Reality and the End of Humanity: Extended Sustainability by the Universal Science of Complexity

- Computer Science
- 2017

The exciting, but rigorously substantiated and objectively inevitable prospects of further civilisation complexity development towards its superior levels of genuine sustainability and global Noosphere are outlined, with practically important conclusions for today's critical problem solution. Expand

#### References

SHOWING 1-10 OF 26 REFERENCES

The Universal Dynamic Complexity as Extended Dynamic Fractality: Causally Complete Understanding of Living Systems Emergence and Operation

- Physics
- 2002

The unreduced description of any real system with interaction reveals natural emergence of multiple, incompatible system versions, or realisations, formed by dynamic entanglement of the interacting… Expand

Universal Symmetry of Complexity and Its Manifestations at Different Levels of World Dynamics

- Physics
- 2003

The unreduced, universally nonperturbative analysis of arbitrary interaction process, described by a quite general equation, provides the truly complete, “dynamically multivalued” general solution… Expand

Chaos and fractals - new frontiers of science

- Mathematics, Computer Science
- 1992

This book discusses Fractal Image Compression, the Causality Principle, Deterministic Laws and Chaos, and the Backbone of Fractals. Expand

Dynamical properties of fractal networks: Scaling, numerical simulations, and physical realizations

- Physics
- 1994

This article describes the advances that have been made over the past ten years on the problem of fracton excitations in fractal structures. The relevant systems to this subject are so numerous that… Expand

Dynamically Multivalued Self-Organisation and Probabilistic Structure Formation Processes

- Physics
- 2004

The unreduced, universally nonperturbative analysis of arbitrary many-body interaction process reveals the irreducible, purely dynamic source of randomness. It leads to the universal definition of… Expand

Fractals in Biology and Medicine

- Biology
- 1994

Fractal Landscapes in Physiology & Medicine: Long-Range Correlations in DNA Sequences and Heart Rate Intervals, and how it can be Tuned and Measured. Expand

Universal concept of complexity by the dynamic redundance paradigm: Causal randomness, complete wave mechanics, and the ultimate unification of knowledge

- Physics
- 1997

The fundamental impasses and ruptures in various domains of the canonical, unitary science, or the 'end of science', become the more and more evident. The natural unity of being is recovered within a… Expand

Chaos and Fractals

- 1987

My talk is a survey of the mathematical work done in our laboratory in the past 10 years. We are not mathematical biologists; rather, we work in mathematics, while maintaining a close relationship… Expand

Increasing biological complexity is positively correlated with the relative genome-wide expansion of non-protein-coding DNA sequences

- Biology
- Genome Biology
- 2003

It is suggested that introns, intergenic sequences, repeat elements, and genomic DNA previously regarded as genetically inert may be far more important to the evolution and functional repertoire of complex organisms than has been previously appreciated. Expand

Dynamical Diffraction Theory by Optical Potential Methods

- Physics
- 1972

Publisher Summary In the past twenty years, there has been a renewed and steadily increasing interest in dynamical diffraction of X-rays and electrons, which is due partly to the availability of… Expand