Indra's Pearls. The Vision of Felix Klein

This is my first reading of this book. This is a book you can come back to.  My first pass was to look through the beautiful images. I have somewhat superficially read the text. The book is well written. It has multiple levels and components.  It is partitioned in a stepwise manner to proceed  from Mobius transformations from circles to circles , then consideration iterated  pair of Mobius transformation of  disjoint circle pairs, then “kissing pairs” then more generalized approaches.  The important properties (conformal orientation preserving mappings) are discussed. The classifications are explained and the relation of these properties to the dynamic (iterated) behaviour is discussed. This book fits well with Visual Complex Analysis.I found the later chapters difficult and hope to come back to them in the future when I have the happy confluence of time, mood and more education.

Central to the book is the concept of the group and particular subgroups. Fractals, chaos, and other concepts from dynamical systems emerge from this book in a beautiful way. There are also historical vignettes of the key figures in the development of the subject.

The pseudocode is well explained in words, then algorithm. I have only just started to play with this. On a second and subsequent readings I hope to work through the projects that the authors provide.

This seems to have been a long labour of love for the three authors and their collaborators.  My first  read was a pleasure and motivator to learn more.

 

 

I have started to explore some of the code in “Circles, circles everywhere“. Some beautiful images and other resources can be found here.

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