A Concise Introduction to Hypercomplex Fractals

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.

1 Fractal Fundamentls. 2 Complex dynamics and resulting complex fractal sets 3 Mandelbrot sets on a complex plane 4 3D Mandelbrot set 5 Hypercomplex, multicomplex and multihypercomplex fractal sets 6 Applications

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.