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What we have found, and what this book is about, is the fact that the golden ratio does indeed encode many intricate patterns that can be turned into interesting drawings. We have collected 360 of these drawings together in this book. This is an art book meant to stimulate your creativity and imagination. There is no mathematics required. We have included two appendices that contain a very short explanation of some of the mathematics behind the golden ratio and how the images are created. 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These patterns provide a glimpse of the hidden platonic world of mathematics.\u003c\/p\u003e \u003cp\u003eThe book starts with Christoffel words and Sturmian sequences which are derived from the continued fraction expansion of rational and irrational numbers. How this is done is explained very clearly in the book and very little mathematical background is required from the reader.\u003c\/p\u003e \u003cp\u003eThe book moves on to Automatic sequences such as the Thue-Morse and Rudin-Shapiro sequences which are various ways of calculating digital roots of the integers. The first part of the book ends with sequences generated by folding paper.\u003c\/p\u003e \u003cp\u003eTranslating a sequence into drawing instructions is done using a finite automaton. This is a very general method for translating sequences that allows the same sequence to produce many different patterns. No prior experience with finite automata is necessary. All the background needed is explained in the book.\u003c\/p\u003e \u003cp\u003eThe second part of the book is devoted to L-systems which is another way of producing a string of drawing instructions. Here the strings are produced by an iterative symbol substitution process. The images produced often have a self similar fractal structure. It is possible to create many images that resemble plants. The book shows how to use an automaton and context free grammars to systematically look at all L-systems of a particular type.\u003c\/p\u003e \u003cp\u003eAll software used to create the sequences and images in the book are free for readers to download from the book's website at: http: \/\/www.abrazol.com\/books\/patterngen\/\u003c\/p\u003e \u003cp\u003eThe software consists of small programs written in the C programming language that can be run on all major operating systems. Inside the book are 327 images serving as inspiration for the kinds of images you can create. 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They provide a very superficial introduction to the subject, enough to engage in cocktail party conversation but little else. This book attempts to bridge these two extremes. This book is written for someone who is at least semi-mathematically literate and wants a concise introduction to some of the major concepts in information theory. The level of mathematics needed is very elementary. A rudimentary grasp of logarithms, probability, and basic algebra is all that is required. Two chapters at the end of the book provide a review of everything the reader needs to know about logarithms and discrete probability to get the most out of the book. Very little attention is given to mathematical proof. Instead the results are presented in a way that makes them almost obvious or at least plausible. The book will appeal to anyone looking for a fast introduction to most of the major topics in information theory. 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This simplicity means that many questions about coin tossing can be asked and answered in great depth, serving as a gateway for exploring probability and statistics, and a foundation for understanding many kinds of probability distributions.\u003c\/p\u003e\u003cp\u003eThis book is an update to the author's original coin toss book (The Coin Toss: Probabilities and Patterns), expanding on run distributions and statistics, as well as a new chapter containing 26 problems and solutions. The page count has increased by over 40 percent.\u003c\/p\u003e\u003cp\u003eThe book contains material for both the beginning student and the advanced researcher. We suspect that the beginner will find some of the material quite difficult and not accessible on a first reading. This is a book that needs to be read more than once. There is more material here than anyone could absorb on a first reading. 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It contains over 200 combinatorics problems with detailed solutions.\u003c\/p\u003e \u003cp\u003eCombinatorics is that part of mathematics that involves counting. It is therefore a fundamental part of math, and mastering it gives you wide reaching powers. The applications of combinatorics include: probability, cryptography, error correcting, games, music, and visual art. It can help you understand other parts of math from a more fundamental perspective.\u003c\/p\u003e \u003cp\u003eThe book begins with the basics of what is needed to solve combinatorics problems, including: definitions, a guide (or classification system) for solving problems based on the twelvefold way, as well as an overview of combinatorics.\u003c\/p\u003e \u003cp\u003eThe remainder of the book consists of problems and solutions. There are 2 separate groups of problems in this book. The first group consists of 82 problems, while the second group has another 124 problems (called exercises). 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