9,820 research outputs found
Fractal dimension evolution and spatial replacement dynamics of urban growth
This paper presents a new perspective of looking at the relation between
fractals and chaos by means of cities. Especially, a principle of space filling
and spatial replacement is proposed to explain the fractal dimension of urban
form. The fractal dimension evolution of urban growth can be empirically
modeled with Boltzmann's equation. For the normalized data, Boltzmann's
equation is equivalent to the logistic function. The logistic equation can be
transformed into the well-known 1-dimensional logistic map, which is based on a
2-dimensional map suggesting spatial replacement dynamics of city development.
The 2-dimensional recurrence relations can be employed to generate the
nonlinear dynamical behaviors such as bifurcation and chaos. A discovery is
made that, for the fractal dimension growth following the logistic curve, the
normalized dimension value is the ratio of space filling. If the rate of
spatial replacement (urban growth) is too high, the periodic oscillations and
chaos will arise, and the city system will fall into disorder. The spatial
replacement dynamics can be extended to general replacement dynamics, and
bifurcation and chaos seem to be related with some kind of replacement process.Comment: 17 pages, 5 figures, 2 table
A Bohmian approach to quantum fractals
A quantum fractal is a wavefunction with a real and an imaginary part
continuous everywhere, but differentiable nowhere. This lack of
differentiability has been used as an argument to deny the general validity of
Bohmian mechanics (and other trajectory--based approaches) in providing a
complete interpretation of quantum mechanics. Here, this assertion is overcome
by means of a formal extension of Bohmian mechanics based on a limiting
approach. Within this novel formulation, the particle dynamics is always
satisfactorily described by a well defined equation of motion. In particular,
in the case of guidance under quantum fractals, the corresponding trajectories
will also be fractal.Comment: 19 pages, 3 figures (revised version
Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience
This essay is presented with two principal objectives in mind: first, to
document the prevalence of fractals at all levels of the nervous system, giving
credence to the notion of their functional relevance; and second, to draw
attention to the as yet still unresolved issues of the detailed relationships
among power law scaling, self-similarity, and self-organized criticality. As
regards criticality, I will document that it has become a pivotal reference
point in Neurodynamics. Furthermore, I will emphasize the not yet fully
appreciated significance of allometric control processes. For dynamic fractals,
I will assemble reasons for attributing to them the capacity to adapt task
execution to contextual changes across a range of scales. The final Section
consists of general reflections on the implications of the reviewed data, and
identifies what appear to be issues of fundamental importance for future
research in the rapidly evolving topic of this review
A Novel Chaotic Image Encryption using Generalized Threshold Function
In this paper, after reviewing the main points of image encryption and
threshold function, we introduce the methods of chaotic image encryption based
on pseudorandom bit padding that the bits be generated by the novel generalized
threshold function (segmentation and self-similarity) methods. These methods
decrease periodic effect of the ergodic dynamical systems in randomness of the
chaotic image encryption. The essential idea of this paper is that given
threshold functions of the ergodic dynamical systems. To evaluate the security
of the cipher image of this scheme, the key space analysis, the correlation of
two adjacent pixels and differential attack were performed. This scheme tries
to improve the problem of failure of encryption such as small key space and
level of security.Comment: 7 pages, 5 figures, Published in international Journal of Computer
Applications (March 2012
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