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.

The following videos illustrate the treasures:
Kaleidoscopes: Ice crystals, Five-fold rotational
Evolutions: Crystal growth, DNA
Assorted growth-decay: radial, rotational

“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.”

— Dr. Daniele Veneziano
Professor of Civil and Environmental Engineering
Massachusetts Institute of Technology

“Patterns abound in our lives, although generally we are not conscious of their presence or their impact. The normal, or Gaussian, distribution is a common pattern familiar not only to statisticians, but to other social and natural scientists as well. It is often so ingrained in us that we tend to take its beauty and grace for granted.”

“Treasures Inside the Bell depicts another form of beauty found in the bell curve using fractals through iteration and interpolating wires. The book’s introduction describes the process at a simple level, with technical details appearing in the third and final chapter. The middle chapter is an aesthetically pleasing “gallery of designs” generated by varying the interpolating points, the parameters, and the resolution. The gallery is subdivided into radial, rotational, and evolutional patterns. 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 may appreciate and marvel at another magnificent facet of the normal distribution.”

— Dr. Carolyn Pillers Dobler and Dr. Russell V. Lenth
Gustavus Adolphus College and University of Iowa
The American Statistician, Volume 50, No.1.

“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.”

— Dr. William A Dembski
Senior Fellow
Discovery Institute's Center for Science and Culture

“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'.”

— Dr. Michael Field
Professor of Mathematics, co-author of Symmetry in Chaos
University of Houston

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

— Mathematical Reviews

Cover art by Fernando Duarte. Page design by Guillermo Jiménez and Segundo.