- Author : Gretchen Boxdorfer
- Publisher :
- Release : 2021
- ISBN :
- Pages : 0 pages
A Study of Visualization Approaches and Fractal Dimension Classification of Certain Boolean Networks
Download or read book A Study of Visualization Approaches and Fractal Dimension Classification of Certain Boolean Networks written by Gretchen Boxdorfer and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boolean Networks provide a simple yet effective approach to the analysis of many complex dynamical systems. And yet, this approach is not currently utilized as widely as possible in various fields. Whether due to lack of knowledge about Boolean Networks or lack of proper modeling software, researchers outside of mathematics may not be able to use this tool that could potentially help with solutions in their own field of knowledge. The main goal of this thesis is to explain the basics of Cellular Automaton and Boolean Networks in a way that requires little mathematical background, making the concepts of these topics accessible to many. Recognizing that visual aides and key to deeper understanding of these concepts, we provide a brief overview of some of the currently available visualization software; asw well as explore some potential additions and propose some possible modifications to these visualization approaches. Furthermore, we outline the basics of fractals and fractal dimensions, and explore how Boolean Networks may be thought of within this framework. We detail the calculation of fractal dimentions of certain Boolean Networks and examine the correlation between fractal dimension and some aspects of the network dynamics. Specifically, we explore the relationship between fractal dimensions and Wolfram's 4 classes of Elementary Cellular Automaton behavior. Our findings match and complement previous work on the topic, and are an indication that fractal dimensions are a meaningful measure of network dynamics, the implication of this being that it may be possible to quantify complex networks using simple measures. The goal is to improve communication surrounding the discourse of Boolean Networks and their utility both among non-mathematicians, and between mathematicians and others. Some applications for Boolean Networks are detailed, including suggested modeling software and use of new findings for these fields.