Related papers: Fractal dimension versus process complexity
It is wellknown that the ordinary calculus is inadequate to handle fractal structures and processes and another suitable calculus needs to be developed for this purpose. Recently it was realized that fractional calculus with suitable…
While numerous examples of fractal spaces may be found in various fields of science, the flow of time is typically assumed to be one-dimensional and smooth. Here we present a metamaterial-based physical system, which can be described by…
The image fractal analysis is actively used in all science branches. In particular in materials science the fractal analysis is applied to study microstructure of deformed metals because its structure can be interpreted as the fractal…
The soft condensed matter of biological organisms exhibits atomic motions whose properties depend strongly on temperature and hydration conditions. Due to the superposition of rapidly fluctuating alternative motions at both very low…
Urbanization is a phenomenon of concern for planning and public health: projections are difficult because of policy changes and natural events, and indicators are multiple. There are previous studies of development that used fractals, but…
This article deals with the estimation of fractal dimension of spatio-temporal patterns that are generated by numerically solving the Swift Hohenberg (SH) equation. The patterns were converted into a spatial series (analogous to time…
The local structure of a fractal set is described by its dimension $D$, which is the exponent of a power-law relating the mass ${\cal N}$ in a ball to its radius $\epsilon$: ${\cal N}\sim \epsilon^D$. It is desirable to characterise the…
The dark silicon problem, which limits the power-growth of future computer generations, is interpreted as a heat energy transport problem when increasing the energy emitting surface area within a given volume. A comparison of two…
Complexity is often invoked alongside size and mass as a characteristic of macroscopic quantum objects. In 2004, Aaronson introduced the \textit{tree size} (TS) as a computable measure of complexity and studied its basic properties. In this…
In this paper we have defined one function that has been used to construct different fractals having fractal dimensions between 1.58 and 2. Also, we tried to calculate the amount of increment of fractal dimension in accordance with the base…
First, let the fractal dimension D=n(integer)+d(decimal), so the fractal dimensional matrix was represented by a usual matrix adds a special decimal row (column). We researched that mathematics, for example, the fractal dimensional linear…
We treat observable operator models (OOM) and their non-commutative generalisation, which we call NC-OOMs. A natural characteristic of a stochastic process in the context of classical OOM theory is the process dimension. We investigate its…
Fractal dimension constitutes the main tool to test for fractal patterns in Euclidean contexts. For this purpose, it is always used the box dimension, since it is easy to calculate, though the Hausdorff dimension, which is the oldest and…
A multifractal analysis is performed on a three-dimensional grayscale image associated with a complex system. First, a procedure for generating 3D synthetic images (2D image stacks) of a complex structure exhibiting multifractal behaviour…
There are three important types of structural properties that remain unchanged under the structural transformation of condensed matter physics and chemistry. They are the properties that remain unchanged under the structural periodic…
This work presents a novel descriptor for texture images based on fractal geometry and its application to image analysis. The descriptors are provided by estimating the triangular prism fractal dimension under different scales with a weight…
Although geographic features, such as mountains and coastlines, are fractal, some studies have claimed that the fractal property is not universal. This claim, which is false, is mainly attributed to the strict definition of fractal…
Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display…
The paper reviews two prominent approaches for the measurement of technological complexity: the method of reflection and the assessment of technologies' combinatorial difficulty. It discusses their central underlying assumptions and…
Urban form and growth can be described with fractal dimension, which is a measurement of space filling of urban evolution. Based on empirical analyses, a discovery is made that the time series of fractal dimension of urban form can be…