Concise Introduction to Hypercomplex Fractals 1st editon by Andrzej Katunin – Ebook PDF Instant Download/Delivery: 1351801201, 9781351801201
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ISBN 10: 1351801201
ISBN 13: 9781351801201
Author: Andrzej Katunin
This book presents concisely the full story on complex and hypercomplex fractals, starting from the very first steps in complex dynamics and resulting complex fractal sets, through the generalizations of Julia and Mandelbrot sets on a complex plane and the Holy Grail of the fractal geometry – a 3D Mandelbrot set, and ending with hypercomplex, multicomplex and multihypercomplex fractal sets which are still under consideration of scientists. I tried to write this book in a possibly simple way in order to make it understandable to most people whose math knowledge covers the fundamentals of complex numbers only. Moreover, the book is full of illustrations of generated fractals and stories concerned with great mathematicians, number spaces and related fractals. In the most cases only information required for proper understanding of a nature of a given vector space or a construction of a given fractal set is provided, nevertheless a more advanced reader may treat this book as a fundamental compendium on hypercomplex fractals with references to purely scientific issues like dynamics and stability of hypercomplex systems.
Concise Introduction to Hypercomplex Fractals 1st Table of contents:
Chapter 1 Introduction to Fractals on a Complex Plane
1.1 Birth of Complex Fractals – Julia and Fatou Sets
1.1.1 Preliminaries
1.1.2 Coloring Fractal Sets on a Complex Plane
1.1.3 Julia and Fatou Sets within the Polynomials of Various Orders
1.1.4 Other Variations of Julia and Fatou Sets on a Complex Plane
1.2 Fractal Revolution – The Mandelbrot Set
1.2.1 History and Concept of the Mandelbrot Set
1.2.2 Geometrical Structure and Atoms of the Mandelbrot Set
1.2.3 Mandelbrot Set within the Polynomials of Various Orders and Other Variations
1.3 Searching for the Holy Grail-3-D Mandelbrot Set
1.4 What’s Next? Further Extensions of the Mandelbrot Set
Chapter 2 Fractal Beasts in Terms of Normed Division and Clifford Algebras
2.1 Quaternionic Fractal Sets
2.1.1 History and Preliminaries of Quaternion Calculus
2.1.2 Quaternionic Julia and Mandelbrot Sets
2.2 Octonionic Fractal Sets
2.2.1 History and Preliminaries of Octonions
2.2.2 Octonionic Julia and Mandelbrot Sets
2.3 Is there Anything Alive in Higher-Dimensional Hypercomplex Spaces?
2.3.1 Preliminaries to Clifford Algebras
2.3.2 Cliffordean Hypercomplex Fractal Sets
2.4 The Places (and hyperspaces) where Fractals Cannot Live
Chapter 3 Tensor Product Fractal Mutants
3.1 Bicomplex, Tricomplex, … Multicomplex Fractal Sets
3.1.1 Julia and Mandelbrot Sets in Bicomplex Vector Space
3.1.2 Julia and Mandelbrot Sets in Tricomplex Vector Space
3.1.3 Julia and Mandelbrot Sets in Multicomplex Vector Space
3.2 Tensor Product Hypercomplex and Multihypercomplex Fractal Sets
3.2.1 Julia and Mandelbrot Sets in Biquaternionic Vector Space
3.2.2 Beyond Biquaternionic Julia and Mandelbrot Sets
Bibliography
Index
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