atural structures are often hierarchical, for example, with a sponge-like topology. Self-similar topologies can be mathematically well described by fractal geometry1. Let us consider objects of a specifi ed family, for example, cracks and fragments2 or dislocation cells3, having a size larger than a given value; self-similar structures imply an inverse proportionality between the number of objects and their size raised to a positive real number D, the so-called fractal exponent (Table 1, fractal law). Interestingly, similar laws can be found in nature with respect to time, not only to space, that is, they describe the distribution of the number of events (earthquakes, for example) having a duration larger than a given value
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exp...
[[abstract]]We provide a direct quantitative evidence that the critical behavior of the Ising model ...
Fractals, 1/f noise, and Zipf's laws are frequently observed within the natural living world as...
Fractal is a set, which geometric pattern is self-similar at different scales. It has a fractal dime...
Many objects in nature, from mountain landscapes to electrical breakdown and turbulence, have a self...
Fractals fascinates both academics and art lovers. They are a form of chaos. A key feature that dist...
Lengths of all caves in a region have been observed previously to be distributed hyperbolically, lik...
In the Solid Earth, fracturing is a pervasive phenomenon : weathering, explosion, impact, faulting, ...
Objects in nature are often very irregular, so that, within the constraints of Euclidean geometry, o...
The term fractal was first coined by the Polish-born, French-American mathe- matician Benoît Mandelb...
The basic rules of central place networks are abstracted and formulated as three geometric series sc...
The most recently completed redshift surveys, such as 2dFGRS, reveal spectacularly complex structure...
The work is the second part of a previous one, published in the same magazine (Contextos I...
The proposed analysis is based on modelling a material with self-similar structure by a continuum se...
Abstract The spatial fractal dimension D of earthquakes (or faults) is often cor-related with the sl...
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exp...
[[abstract]]We provide a direct quantitative evidence that the critical behavior of the Ising model ...
Fractals, 1/f noise, and Zipf's laws are frequently observed within the natural living world as...
Fractal is a set, which geometric pattern is self-similar at different scales. It has a fractal dime...
Many objects in nature, from mountain landscapes to electrical breakdown and turbulence, have a self...
Fractals fascinates both academics and art lovers. They are a form of chaos. A key feature that dist...
Lengths of all caves in a region have been observed previously to be distributed hyperbolically, lik...
In the Solid Earth, fracturing is a pervasive phenomenon : weathering, explosion, impact, faulting, ...
Objects in nature are often very irregular, so that, within the constraints of Euclidean geometry, o...
The term fractal was first coined by the Polish-born, French-American mathe- matician Benoît Mandelb...
The basic rules of central place networks are abstracted and formulated as three geometric series sc...
The most recently completed redshift surveys, such as 2dFGRS, reveal spectacularly complex structure...
The work is the second part of a previous one, published in the same magazine (Contextos I...
The proposed analysis is based on modelling a material with self-similar structure by a continuum se...
Abstract The spatial fractal dimension D of earthquakes (or faults) is often cor-related with the sl...
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exp...
[[abstract]]We provide a direct quantitative evidence that the critical behavior of the Ising model ...
Fractals, 1/f noise, and Zipf's laws are frequently observed within the natural living world as...