A Fractal Excursion

1991 ◽  
Vol 84 (4) ◽  
pp. 265-275
Author(s):  
Dane R. Camp
Keyword(s):  
Chaos Theory ◽  
Fractal Geometry ◽  
Equilateral Triangle ◽  
Related Topic ◽  
Self Similarity ◽  
Koch Curve ◽  
Fields Of Study ◽  
Simple Recursion ◽  
Mathematics And Physics

Recently, chaos theory and the related topic of fractal geometry have blossomed as creative fields of study in mathematics and physics. Fractals are shapes containing self-similarity on arbitrary magnification. One such object, the Koch curve, is generated by simple recursion on an equilateral triangle. The process used to produce the curve is a great way to introduce students to some concepts of fractal geometry.

An Exercise in a Transdisciplinary Approach for New Knowledge Paradigms

2014 ◽  
Vol 3 (3) ◽  
pp. 114-143
Author(s):  
Gabriel Crumpei ◽  
Maricel Agop ◽  
Alina Gavriluţ ◽  
Irina Crumpei
Keyword(s):  
Quantum Mechanics ◽  
20Th Century ◽  
Chaos Theory ◽  
Fractal Geometry ◽  
Science And Religion ◽  
Transdisciplinary Approach ◽  
Linear Dynamics ◽  
New Knowledge ◽  
Religious Perspectives ◽  
Energy Information

Abstract In this paper, we aim at an exercise that is transdisciplinary, involving science and religion, and interdisciplinary, involving disciplines and theories which appeared in the second half of the 20th century (e.g., topology, chaos theory, fractal geometry, non-linear dynamics, all of which can be found in the theory of complex systems). The latter required the reformulation of quantum mechanics theories starting with the beginning of the century, based on the substance-energy-information triangle. We focus on information and we also attempt a transdisciplinary approach to the imaginary from a psychological - physical - mathematical perspective, but the religious perspectives find their place along with the philosophical or even philological vision

Similarity Hashing: A Computer Vision Solution to the Inverse Problem of Linear Fractals

Fractals ◽  
1997 ◽  
Vol 05 (supp01) ◽  
pp. 39-50 ◽  
Author(s):  
John C. Hart ◽  
Wayne O. Cochran ◽  
Patrick J. Flynn
Keyword(s):  
Computer Vision ◽  
Inverse Problem ◽  
Heuristic Search ◽  
Fractal Geometry ◽  
Self Similarity ◽  
Geometric Hashing ◽  
Numerical Minimization ◽  
Self Similar ◽  
Vision Algorithm ◽  
Fractal Representation

The difficult task of finding a fractal representation of an input shape is called the inverse, problem of fractal geometry. Previous attempts at solving this problem have applied techniques from numerical minimization, heuristic search and image compression. The most appropriate domain from which to attack this problem is not numerical analysis nor signal processing, but model-based computer vision. Self-similar objects cause an existing computer vision algorithm called geometric hashing to malfunction. Similarity hashing capitalizes on this observation to not only detect a shape's morphological self-similarity but also find the parameters of its self-transformations.

Fractal Study on the Complexity of Limestone Surface Pore Structure

2012 ◽  
Vol 548 ◽  
pp. 275-280
Author(s):  
Xin Wu ◽  
Si Long ◽  
Guo Hui Li
Keyword(s):  
Fractal Dimension ◽  
Rock Mass ◽  
Pore Structure ◽  
Fractal Geometry ◽  
Fractal Theory ◽  
Microscopic Images ◽  
Simple Rules ◽  
Complex Phenomena ◽  
Mathematics And Physics

Complex characteristics of pore structure of rock mass, such as limestone, are difficult to describe by means of general mathematics and physics. While, the fractal geometry can describe some simple rules behind complex phenomena; and these simple rules can describe the complex phenomena. Therefore in this paper, the fractal theory is applied to study the complexity of the limestone pore structure. Through calculating the fractal dimension of the limestone pore microscopic images of different zoom scales, the scale-independence is proved to be possessed by complexity of pore, which indicates that the limestone is a good fractal body, and its complexity can be studied by means of fractal dimension.

scholarly journals Design and Testing of Fractal Antenna Parameters based on the Koch Curve for Reception of Digital Terrestrial Television Signals in the UHF Band

2019 ◽  
Vol 11 (1) ◽  
pp. 159-172
Author(s):  
Pablo Lupera Morillo ◽  
Gary Flores Cadena ◽  
Ricardo Merizalde
Keyword(s):  
Fractal Geometry ◽  
Laboratory Tests ◽  
Network Analyzer ◽  
Fractal Antenna ◽  
Koch Curve ◽  
Radiation Characteristics ◽  
Digital Terrestrial Television ◽  
To Receive ◽  
Design And Testing ◽  
Uhf Band

Purpose – In this research paper, the electrical and radiation characteristics of a proposed fractal antenna based on the Koch curve in the second iteration for reception of digital terrestrial television signals are designed and analyzed by laboratory tests. Methodology/approach/design – The design is based on the concepts of fractal geometry and on a previously designed antenna, which is adapted to obtain a different frequency of operation; the designed antenna is constructed in three different ways, finally, they are tested in the lab using vector-network-analyzer, that allows to measure parameters, such as: VSWR, gain and radiation pattern. Findings – The fractal antenna based on the Koch curve has the necessary characteristics to receive digital terrestrial television signals in the UHF band.

scholarly journals A new method to improve feature selection with meta-heuristic algorithm and chaos theory

2018 ◽  
Vol 7 (1) ◽  
pp. 9-24
Author(s):  
Mohammad Masoud Javidi
Keyword(s):  
Feature Selection ◽  
Evolutionary Algorithms ◽  
Random Process ◽  
Chaos Theory ◽  
Heuristic Algorithms ◽  
Large Data ◽  
Data Set ◽  
Suitable Alternative ◽  
Optimal Subset ◽  
Fields Of Study

Finding a subset of features from a large data set is a problem that arises in many fields of study. It is important to have an effective subset of features that is selected for the system to provide acceptable performance. This will lead us in a direction that to use meta-heuristic algorithms to find the optimal subset of features. The performance of evolutionary algorithms is dependent on many parameters which have significant impact on its performance, and these algorithms usually use a random process to set parameters. The nature of chaos is apparently random and unpredictable; however it also deterministic, it can suitable alternative instead of random process in meta-heuristic algorithms

scholarly journals Deterministic Chaos Theory: Basic Concepts

2016 ◽  
Vol 39 (1) ◽  
Author(s):  
Mauro Cattani ◽  
Iberê Luiz Caldas ◽  
Silvio Luiz de Souza ◽  
Kelly Cristiane Iarosz
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Chaos Theory ◽  
Initial Conditions ◽  
Nonlinear Differential Equations ◽  
Deterministic Chaos ◽  
Chaotic Motions ◽  
And Mathematics ◽  
Irregular Behavior ◽  
Mathematics And Physics

This article was written to students of mathematics, physics and engineering. In general, the word chaos may refer to any state of confusion or disorder and it may also refer to mythology or philosophy. In science and mathematics it is understood as irregular behavior sensitive to initial conditions. In this article we analyze the deterministic chaos theory, a branch of mathematics and physics that deals with dynamical systems (nonlinear differential equations or mappings) with very peculiar properties. Fundamental concepts of the deterministic chaos theory are briefly analyzed and some illustrative examples of conservative and dissipative chaotic motions are introduced. Complementarily, we studied in details the chaotic motion of some dynamical systems described by differential equations and mappings. Relations between chaotic, stochastic and turbulent phenomena are also commented.

scholarly journals Introdução à Geometria Fractal no Ensino Médio Técnico: Uma Abordagem com Programação Python

2021 ◽  
Author(s):  
Gustavo Vieira Ferreira ◽  
Weliton Dal Pizzol Maria ◽  
Adriano Rodrigues de Melo
Keyword(s):  
High School ◽  
Fractal Geometry ◽  
Cantor Set ◽  
Koch Curve ◽  
Analytical Geometry ◽  
Technical High School ◽  
Sierpinski Triangle ◽  
Python Language ◽  
Fractal Patterns ◽  
Bibliographic Search

This work is inserted in the context of technical high school andit aimed to analyze the integration between the branches of FractalGeometry, Analytical Geometry and Computer Programming.For this purpose, we carried out a bibliographic search about whatcharacterizes and distinguishes Fractal Geometry from EuclideanGeometry, we also seek in our readings to list the most famousfractals. Then, we developed (in python language) several fractalgeneration programs. It was possible to work with amazing andeasily programmable fractal shapes, such as the Cantor Set, theHilbert Curve and Sierpinski Triangle. We also built two new familiesof fractal shapes from a generalization of the Koch Curve. Weconclude that programming fractals in the context of technical highschool is productive and challenging, as it requires many changesin the representations of fractal patterns.

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