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Concise Introduction to Hypercomplex Fractals [Kõva köide]

  • Formaat: Hardback, 91 pages, kõrgus x laius: 234x156 mm, kaal: 320 g, 6 Tables, black and white; 1 Halftones, color; 53 Illustrations, color; 2 Illustrations, black and white
  • Ilmumisaeg: 10-Oct-2017
  • Kirjastus: CRC Press
  • ISBN-10: 1138633429
  • ISBN-13: 9781138633421
Teised raamatud teemal:
Concise Introduction to Hypercomplex FractalsSuurem pilt
  • Formaat: Hardback, 91 pages, kõrgus x laius: 234x156 mm, kaal: 320 g, 6 Tables, black and white; 1 Halftones, color; 53 Illustrations, color; 2 Illustrations, black and white
  • Ilmumisaeg: 10-Oct-2017
  • Kirjastus: CRC Press
  • ISBN-10: 1138633429
  • ISBN-13: 9781138633421
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781138633421.html
Märksõnad:
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.
Preface vii
Chapter 1 Introduction to Fractals on a Complex Plane
1(36)
1.1 Birth of Complex Fractals -- Julia and Fatou Sets
3(16)
1.1.1 Preliminaries
3(3)
1.1.2 Coloring Fractal Sets on a Complex Plane
6(6)
1.1.3 Julia and Fatou Sets within the Polynomials of Various Orders
12(4)
1.1.4 Other Variations of Julia and Fatou Sets on a Complex Plane
16(3)
1.2 Fractal Revolution -- The Mandelbrot Set
19(10)
1.2.1 History and Concept of the Mandelbrot Set
19(1)
1.2.2 Geometrical Structure and Atoms of the Mandelbrot Set
20(5)
1.2.3 Mandelbrot Set within the Polynomials of Various Orders and Other Variations
25(4)
1.3 Searching For the Holy Grail -- 3-D Mandelbrot Set
29(4)
1.4 What's Next? Further Extensions of the Mandelbrot Set
33(4)
Chapter 2 Fractal Beasts in Terms of Normed Division and Clifford Algebras
37(26)
2.1 Quaternionic Fractal Sets
38(11)
2.1.1 History and Preliminaries of Quaternion Calculus
38(1)
2.1.2 Quaternionic Julia and Mandelbrot Sets
39(10)
2.2 Octonionic Fractal Sets
49(6)
2.2.1 History and Preliminaries of Octonions
49(2)
2.2.2 Octonionic Julia and Mandelbrot Sets
51(4)
2.3 Is There Anything Alive in Higher-Dimensional Hypercomplex Spaces?
55(3)
2.3.1 Preliminaries to Clifford Algebras
56(1)
2.3.2 Cliffordean Hypercomplex Fractal Sets
57(1)
2.4 The Places (And Hyperspaces) Where Fractals Cannot Live
58(5)
Chapter 3 Tensor Product Fractal Mutants
63(30)
3.1 Bicomplex, Tricomplex, Multicomplex Fractal Sets
63(10)
3.1.1 Julia and Mandelbrot Sets in Bicomplex Vector Space
63(7)
3.1.2 Julia and Mandelbrot Sets in Tricomplex Vector Space
70(2)
3.1.3 Julia and Mandelbrot Sets in Multicomplex Vector Space
72(1)
3.2 Tensor Product Hypercomplex and Multihypercomplex Fractal Sets
73(20)
3.2.1 Julia and Mandelbrot Sets in Biquaternionic Vector Space
73(5)
3.2.2 Beyond Biquaternionic Julia and Mandelbrot Sets
78(3)
Bibliography
81(12)
Index 93
Prof. Andrzej Katunin received B.Sc. (2006) in mechanical engineering from Bialystok University of Technology, Poland, and the M.Sc. (2008), Ph.D. (2012) and D.Sc. (2015) in the same discipline from Silesian University of Technology, Poland. His scientific works on fractals cover both purely mathematical studies as well as application issues in computer graphics and various engineering fields.