Introduction to Fractal Geometry .................................................................. 1 1. A few Random Quotes ......................................................................... 1 2. Introduction ....................................................................................... 1 3. Types of fractals ........................................................................

A fractal is an object or a structure that is self-similar in all length scales. Fractal geometry is an excellent mathematical tool used in the study of irregular geometric objects. The concept of the fractal dimension, D, as a measure of complexity is defined. The concept of fractal geometry is closely linked to scale invariance, and it provides a framework for the analysis of natural phenomen...

Fractal structure of the six-vertex model is introduced with the use of the IFS (Iterated Function Systems). The fractal dimension satisfies an equation written by the free energy of the six-vertex model. It is pointed out that the transfer matrix method and the n-equivalence relation introduced in lattice theories have also been introduced in the area of fractal geometry. All the results can b...

Iterated function systems have been at the heart of fractal geometry almost from its origins. The purpose of this expository article is to discuss new research trends that are at the core of the theory of iterated function systems (IFSs). The focus is on geometrically simple systems with finitely many maps, such as affine, projective andMöbius IFSs. There is an emphasis on topological and dynam...

1. Introduction Many natural structures cannot be described by conventional methods, because they are complex and irregular. Relatively a new approach is the application of fractal geometry [1]–[3]. This geometry is successfully used in science, but an application in industry is sporadic and experimental only. However, the fractal geometry can be used as a useful tool for an explicit, objective...

The latest research works have revealed that fractal geometry, a measure of irregular contours, inconvenient for describing the various pathological architectures like tumors (for yielding insights into the tumor growth), different MR (magnetic-response) image analysis, neuro imaging analysis, bone fracture measurement and many more. Researchers major attraction towards fractal geometry lie in ...

In this paper, we introduce an L-system based on the fractal geometry to study complex fracture networks. Comparing with other simulation models, the fractal fracture could not only maintain the bifurcation of the fracture geometry but also represent the multi-level feature of the complex fracture networks according to its fractal characteristics. Since the fractal geometry is always connected ...

Psychological and physiological benefits of viewing nature have been extensively studied for some time. More recently it has been suggested that some of these positive effects can be explained by nature's fractal properties. Virtually all studies on human responses to fractals have used stimuli that represent the specific form of fractal geometry found in nature, i.e. statistical fractals, as o...

Fractal antennas have been shown to demonstrate repetitive multi-band or logperiodic behavior that has been attributed to the self-similar scale factor of the antenna’s geometry. This geometry, which has been used to model complex objects found in nature such as clouds and coastlines, has space filling properties that can be utilized to miniaturize antennas. These unique properties of fractals ...

The idea of buildings in harmony with nature can be traced back to ancient times. The increasing concerns on sustainability oriented buildings have added new challenges in building architectureral design and called for new design responses. Sustainable design integrates and balances the human geometries and the natural ones. As the language of nature, it is, therefore, natural to assume that fr...