Why is topography fractal

Fractals in Geophysics pp Cite as. The scale invariant properties of fractal sets make them attractive models for topographic profiles because those profiles are the end product of a complex system of physical processes operating over many spatial scales.

The power spectra from a Digital Elevation Model 30 meter sample spacing of the Sierra Nevada Batholith and from Seabeam center beam depths meter sample spacing along a flowline in the South Atlantic are curved.

Straight sections in the spectra can be identified but the slopes of those sections are strongly dependent upon the particulars of the data analysis. Fractal geometry must be used with caution in the discussion of topographic data sets. Unable to display preview. Download preview PDF. Skip to main content. This service is more advanced with JavaScript available. Advertisement Hide. Are Topographic Data Sets Fractal? Song, C. Scaling of degree correlations and its influence on diffusion in scale-free networks.

Galvao, V. Modularity map of the network of human cell differentiation. Proceedings of the National Academy of Sciences , — Gallos, L.

The conundrum of functional brain networks: Small-world efficiency or fractal modularity. Frontiers in Physiology 3 , Article Google Scholar. Ma, D. Power-law scaling and fractal nature of medium-range order in metallic glasses. China Earth Sci. Wang, B. Derivation of permeability-pore relationship for fractal porous reservoirs using series-parallel flow resistance model and lattice boltzmann method.

Fractals 22 , Dingal, P. Fractal heterogeneity in minimal matrix models of scars modulates stiff-niche stem-cell responses via nuclear exit of a mechanorepressor.

Zheng, X. Multiscale metallic metamaterials. Ding, D. A user-friendly modified pore-solid fractal model. Namazi, H. Fractal based analysis of the influence of odorants on heart activity. Fractal density and singularity analysis of heat flow over ocean ridges. A mathematical model of fluid flow in tight porous media based on fractal assumptions. Carpinteri, A.

Are scaling laws on strength of solids related to mechanics or to geometry? Ghanbarian-Alavijeh, B. Self-affine fractals and fractal dimension. Scripta 32 , — Evaluating the fractal dimension of surfaces. London, Ser. A , — Sreenivasan, K.

Fractals and multifractals in fluid turbulence. Fluid Mech. Download references. You can also search for this author in PubMed Google Scholar. All authors contributed to the writing of the manuscript. Correspondence to Yi Jin. This work is licensed under a Creative Commons Attribution 4. Reprints and Permissions. Sci Rep 7, Download citation. Received : 18 January Accepted : 22 March Published : 24 April Anyone you share the following link with will be able to read this content:. Sorry, a shareable link is not currently available for this article.

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Advanced search. Skip to main content Thank you for visiting nature. Download PDF. Subjects Geophysics Nonlinear phenomena Statistics. Abstract Fractal behavior is scale-invariant and widely characterized by fractal dimension. Introduction Fractals were originally introduced by Mandelbrot 1 to describe the fractal behaviors of similar geometries in disordered and irregular objects such as the natural coastlines 1 , 2 , 3 , phenomena in natural and artificial materials 4 , 5 , 6 , porous media 7 , 8 , 9 , 10 , biological structures 11 , rough surfaces 12 , 13 , 14 , 15 , as well as novel application of factuality to complex networks and brain systems 16 , 17 , Figure 1: Fractals constructed by different fractal generators with the same fractal behaviors or by the same fractal generators with different fractal behaviors.

Full size image. Methods and Discussion To provide a theoretical, mechanistic basis for understanding the property of scale-invariance, we must mathematically define it per the key requirements we have previously laid out. Figure 2. A fractal and its topography for a variant of the Sierpinski gasket. Figure 3: Fractals to demonstrate the validity of Eq.

Table 1 The fractal topography information of classic fractals and their fractal dimensions calculated by Eq. Full size table. Citation Type. Has PDF. Publication Type. More Filters. Most natural landscapes are characterized by multiscale often multifractal topography with well-known scale-invariance properties.

For example, the spectral density of landscape elevation fields is … Expand. View 1 excerpt. Applications and Models. Publisher Summary This chapter focuses on the applications and models of self-affine time series. The chapter presents the stochastic component of time series associated with complex phenomena that … Expand. View 2 excerpts, cites methods and background. Discriminating between the nature of radioactive contamination. Abstract Effective management of radioactive contamination necessitates the accurate classification of the polluting elements.

In many cases, such a classification is not straightforward. The physics … Expand. Fractal mapping of digitized images: Application to the topography of Arizona and comparisons with synthetic images.