Publication

Thermodynamics of fractal networks

1996
Journal Articles

Abstract

Optimal channel networks are fractal structures that bear a striking resemblance to real rivers. They are obtained by minimizing an energy functional associated with spanning trees. We show that large network development effectively occurs al zero temperature since the entropy scales subdominantly with system size compared to the energy. Thus these networks develop under generic conditions and freeze into a static scale-free structure. We suggest a link of optimal channel networks with self-organized critical systems and critical phenomena which exhibit spatial and temporal fractality, the former under generic conditions and the latter on fine tuning.

Official source

https://infoscience.epfl.ch/entities/publication/3905c755-e210-4adb-b74f-0ca71674e1fc

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1996
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/3905c755-e210-4adb-b74f-0ca71674e1fc

About this result

Related concepts (23)

Fractal analysis

Fractal analysis is assessing fractal characteristics of data. It consists of several methods to assign a fractal dimension and other fractal characteristics to a dataset which may be a theoretical dataset, or a pattern or signal extracted from phenomena including topography, natural geometric objects, ecology and aquatic sciences, sound, market fluctuations, heart rates, frequency domain in electroencephalography signals, digital images, molecular motion, and data science. Fractal analysis is now widely used in all areas of science.

Self-organized criticality

Self-organized criticality (SOC) is a property of dynamical systems that have a critical point as an attractor. Their macroscopic behavior thus displays the spatial or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality. The concept was put forward by Per Bak, Chao Tang and Kurt Wiesenfeld ("BTW") in a paper published in 1987 in Physical Review Letters, and is considered to be one of the mechanisms by which complexity arises in nature.

Fractal

In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine self-similar.

Related publications (2)

Thermodynamics of fractal networks

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