About the Author

Carlos E Puente received his PhD in Hydrology from Massachusetts Institute of Technology in 1984. Since then, he has published over 40 journal papers. Some of his most recent works include Chaos and Stochasticity in Deterministically Generated Multifractal Measures for the journal Fractals; DNA, Pi and the Bell for the journal Complexity; and the book The Hypotenuse, an illustrated scientific parable for turbulent times, submitted to Berrett-Koehler. He has also made over 85 presentations at numerous conferences relating to topics in Nonlinear Dynamics and Hydrology.

Generalized versions of the central limit theorem that lead to Gaussian distributions over one and higher dimensions, via arbitrary iterations of simple mappings, have recently been discovered by the author of this publication and his collaborators. Treasures Inside the Bell: Hidden Order in Chance reveals how these new constructions result in infinite exotic kaleidoscopic decompositions of two-dimensional circular bells in terms of beautiful deterministic patterns possessing arbitrary n-fold symmetries. These are patterns that, while reminding us of the infinite structure previously found in the celebrated Mandelbrot set, turn out to contain natural shapes such as snow crystals and biochemical rosettes, and even the DNA structure of life.

Contents:

• Introducing the Bell:
• The Notion of Iterations
• Interpolating Wires
• Textures on Interpolating Wires
• The Bell as a Shadow
• Wires and Bells in Higher Dimensions
• Exotic Patterns Inside the Bell
• Natural Sets Inside the Bell
• More Treasures Inside the Bell
• Gallery Designs:
• Radial Patterns
• Rotational Patterns
• Evolutions & Quilts
• Technical Notes

"Treasures Inside the Bell is in many ways a unique book. It is rooted in mathematics but does not speak only to mathematicians. It deals with esoteric limit theorems and fractal/multifractal constructions, but can be enjoyed by readers with minimal technical background. The book takes the reader through a journey where simple mathematical rules are the doorway to an incredibly varied and aesthetically fascinating world of geometrical patterns, and eventually to the Gaussian distribution (the bell). The journey can be followed through mathematical reasoning, but mathematics is intertwined with aesthetics, philosophy and religion. The quest for a link among geometry, the physical world and deep spiritual principles is at the core of the book. Some readers will find Puente's analogies compelling. Those who do not will be left wondering how disorder can lead to order, chaos to universality, conflict to love and what relates these concepts in mathematics, physics and human life."

"Carlos Puente has a gift for drawing connections and finding patterns. Explore with him as your guide the riches hidden inside the bell curve. You will not be disappointed."

"The paradox is now well established that chaos can often contain (hidden) order and structure. The problem is how to 'see' the structure. In this intriguing and original book, the author finds and describes remarkable symmetric patterns and resonances concealed within one of the signatures of randomness — the bell curve or normal distribution — and along the way makes contact with both natural forms and fundamental constants of mathematics. A sample program is provided for readers to conduct their own explorations of as yet undiscovered 'treasures of the bell'."

"This beautifully illustrated book deals with iterated function systems (IFS), especially those which generate curves representing continuous functions."

“Although the rendition of patterns in the book is static, the accompanying CD allows the reader to view them dynamically. Through these striking and brilliant designs, the reader can appreciate and marvel at another magnificent facet of the normal distribution.”