Classification of Galaxies Using Fractal Dimensions
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UNLV Retrospective Theses & Dissertations 1-1-1999 Classification of galaxies using fractal dimensions Sandip G Thanki University of Nevada, Las Vegas Follow this and additional works at: https://digitalscholarship.unlv.edu/rtds Repository Citation Thanki, Sandip G, "Classification of galaxies using fractal dimensions" (1999). UNLV Retrospective Theses & Dissertations. 1050. http://dx.doi.org/10.25669/8msa-x9b8 This Thesis is protected by copyright and/or related rights. It has been brought to you by Digital Scholarship@UNLV with permission from the rights-holder(s). You are free to use this Thesis in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s) directly, unless additional rights are indicated by a Creative Commons license in the record and/ or on the work itself. 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Thanki Bachelor of Science Widener University 1997 A thesis submitted in partial fulfillment of the requirements for the Master of Science Degree Department of Physics College of Sciences Graduate College University of Nevada, Las Vegas August 1999 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 1396434 UMI Microform 1396434 Copyright 1999, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Thesis Approval The Graduate College University of Nevada, Las Vegas July 29______ .19 99 The Thesis prepared by Sandip G Thanki Entitled Classification of Galaxies Using Fractal Dimensions is approved in partial fulfillment of the requirements for the degree of _______ Master of Science in Physics ______________________ 6 X Examination Committee Chair Dean of the Graduate College Examination Committee M emer Examination Committee Member Graduate College faculty Represematwe 11 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT Classification of Galaxies Using Fractal Dimensions by Sandip Thanki Dr. George Rhee, Examination Committee Chair Assistant Professor University of Nevada, Las Vegas The classification of galaxies is morphological. Shapes of the galaxies range from the very simple (e.g. elliptical galaxies) to the highly complex (e.g. irregular galaxies). Analyzing a measure of complexity for such shapes could lead to automatic classifica tion. Fractal dimension, a quantity related to the complexity of a given shape, could be such a measure. Capacity dimension and correlation dimension are two of the several types of fractal dimensions. In this project, correlation dimensions and the capacity dimensions of the contours generated around different intensity levels of the galaxy images, versus the intensity levels were computed. It was found that elliptical galaxies tend to have a lower value of the average correlation dimension (computed for a selected range of intensity levels) than spirals. Ill Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS ABSTRACT ..................................................................................................................... iii LIST OF TABLES............................................................................................................ vi LIST OF FIGURES.......................................................................................................... ACKNOWLEDGMENTS................................................................................................. viii CHAPTER 1 INTRODUCTION............................................................................... 1 CHAPTER 2 GALAXY CLASSIFICATION SCHEMES .................................... 3 “Tuning Fork” ............................................................................................................ 3 Elliptical Galaxies ............................................................................................ 3 Spiral Galaxies ................................................................................................... 4 Irregular Galaxies .............................................................................................. 5 Other Classification Schemes.................................................................................. 5 CHAPTER 3 FRACTAL DIMENSIONS................................................................. 6 Defining Fractals and Fractal Dimensions............................................................. 6 Capacity Dimension......................................................................................... 9 Correlation Dimension..................................................................................... 10 Calculating Fractal Dimension................................................................................ 11 CHAPTER 4 DATA SET ........................................................................................... 12 CHAPTER 5 FRACTAL DIMENSIONS OF GALAXIES......................... 17 Contour Generation................................................................................................... 17 Calculation of Fractal Dimensions of the Contours............................................. 18 R e su lts .......................................................................................................................... 20 Capacity Dimensions and Correlation Dimensions................................... 20 IV Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Comparing Correlation Dimensions and Capacity Dimensions.............. 23 CHAPTER 6 CONCLUSIONS .................................................................................. 40 REFERENCES................................................................................................................. 42 V IT A .................................................................................................................................... 43 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF TABLES Table 1 Length of the coast of Britain..................................................................... 7 Table 2 Length of a circle with a diameter of 1000 k m ....................................... 8 Table 3 Data set ........................................................................................................... 12 Table 4 NGC 2403 to NGC 3953 (Data for the entire intensity range) 32 Table 5 NGC 4013 to NGC 4527 (Data for the entire intensity range) 33 Table 6 NGC 4535 to NGC 5746 (Data for the entire intensity range) 34 Table 7 NGC 5792 to NGC 6503 (Data for the entire intensity range) 35 Table 8 NGC 2403 to NGC 3953 (Data for a selected intensity range) 36 Table 9 NGC 4013 to NGC 4527 (Data for a selected intensity range) 37 Table 10 NGC 4535 to NGC 5746 (Data for a selected intensity range) 38 Table 11 NGC 5792 to NGC 6503 (Data for a selected intensity range) 39 VI Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF FIGURES Figure 1 Tuning Fork Diagram .................................................................................. 3 Figure 2 Koch curve ......................................................................................................