Related papers: Fractal dimension, and the problems traps of its e…
Predicting when rupture occurs or cracks progress is a major challenge in numerous elds of industrial, societal and geophysical importance. It remains largely unsolved: Stress enhancement at cracks and defects, indeed, makes the macroscale…
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…
A topological bifurcation in chaotic scattering is characterized by a sudden change in the topology of the infinite set of unstable periodic orbits embedded in the underlying chaotic invariant set. We uncover a scaling law for the fractal…
The universal concept of complexity by the dynamic redundance paradigm and the ensuing concept of extended dynamic fractality (physics/9806002) are applied here to higher levels of complexity corresponding to living systems. After recalling…
Many biological processes and objects can be described by fractals. The paper uses a new type of objects - blinking fractals - that are not covered by traditional theories considering dynamics of self-similarity processes. It is shown that…
Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be…
Fractals are ubiquitous natural emergences that have gained increased attention in engineering applications, thanks to recent technological advancements enabling the fabrication of structures spanning across many spatial scales. We show how…
This chapter introduces the fracture nucleation process, their (extreme) statistics in disordered solids, in fiber bundle models, and in the two fractal overlap models of earthquake.
The relevance of chaos to evolution is discussed in the context of the origin and maintenance of diversity and complexity. Evolution to the edge of chaos is demonstrated in an imitation game. As an origin of diversity, dynamic clustering of…
Fractals are geometric shapes that can display complex and self-similar patterns found in nature (e.g., clouds and plants). Recent works in visual recognition have leveraged this property to create random fractal images for model…
It is argued that the occurrence of disproportionately ("un-natural") large (or small) numbers, as well as deep cancellations, are comparatively natural traits of the way Nature is geared to operate in most complex systems. The idea is…
In light of the emergence of big data, I have advocated and argued for a paradigm shift from Tobler's law to scaling law, from Euclidean geometry to fractal geometry, from Gaussian statistics to Paretian statistics, and - more importantly -…
We review the present status of our research and understanding regarding the dynamics and the statistical properties of earthquakes, mainly from a statistical physical viewpoint. Emphasis is put both on the physics of friction and fracture,…
A recent quasiclassical description of a tunneling universe model is shown to exhibit chaotic dynamics by an analysis of fractal dimensions in the plane of initial values. This result relies on non-adiabatic features of the quantum…
Neural network models have recently demonstrated impressive prediction performance in complex systems where chaos and unpredictability appear. In spite of the research efforts carried out on predicting future trajectories or improving their…
This article examines the subtle relationship between chaos and randomness, two concepts that, although they refer to seemingly unpredictable phenomenon, are based on fundamentally different principles. Chaos manifests in deterministic…
Anomalies are occurrences in a dataset that are in some way unusual and do not fit the general patterns. The concept of the anomaly is typically ill-defined and perceived as vague and domain-dependent. Moreover, despite some 250 years of…
Depth is a complexity measure for natural systems of the kind studied in statistical physics and is defined in terms of computational complexity. Depth quantifies the length of the shortest parallel computation required to construct a…
A reliable understanding of the Earth system is essential for the life quality of modern society. Natural hazards are the cause of most life and resource losses. The ability to define the conditions for a sustainable development of…
We analyze the fate of dynamical systems that consist of two kind of processes. The first type is supposed to perform a certain function by processing information at a required high accuracy, which is, however, limited to less than 100…