There are 50 unique patterns in this book, each on its own physical page. Most of the patterns are based on Christoffel words, named after Elwin Bruno Christoffel (1829-1900), a German mathematician and physicist. Details on pattern generation with Christoffel words can be found in the book "Pattern Generation for Computational Art."

This book shows how to turn computer generated number sequences into intricate visual patterns. The sequences are strings of the binary numbers 0 and 1 which are translated into drawing instructions to produce beautiful patterns. These patterns provide a glimpse of the hidden platonic world of mathematics.

The 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.

The 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.

Translating 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.

The 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.

All 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/

The 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. There are an infinite variety of images you can generate using the software that comes with this book, providing a computational image generation lab.

This book is the result of a lifelong love of music and an obsession with patterns. The authors have for many years been exploring methods to find, create, describe and analyze patterns. They wrote this book to show how some of these methods can be used to generate rhythms. The methods can produce an almost endless variety of new rhythms along with popular traditional ones. For a lover of music what could be more wonderful than that?

The study of patterns at anything beyond a superficial level does require some mathematics. Fortunately the mathematics can be kept at a very elementary level. Anyone comfortable with a little algebra should have no trouble understanding and using these rhythm generation methods. Only the last chapter on stochastic rhythms requires a bit more than elementary mathematics. Any reader who faints at the sight of an equation should probably not buy the book.

The book has many example rhythms for which there are MIDI files that you can listen to on the book's website: abrazol.com/books/rhythm1/. There you can also find free software for generating rhythms, doing calculations, and creating MIDI files.

This is a book about solving problems related to automata and regular expressions. It helps you learn the subject in the most effective way possible, through problem solving. There are 84 problems with solutions. The introduction provides some background information on automata, regular expressions, and generating functions. The inclusion of generating functions is one of the unique features of this book. Few computer science books cover the topic of generating functions for automata and there are only a handful of combinatorics books that mention it. This is unfortunate since we believe the connection between computer science and combinatorics, that is opened up by these generating functions, can enrich both subjects and lead to new methods and applications. We cover a few interesting classes of problems for finite state automata and then show some examples of infinite state automata and recursive regular expressions. The final problem in the book involves constructing a recursive regular expression for matching regular expressions. This book explains: * Why automata are important. * The relationship of automata to regular expressions. * The difference between deterministic and nondeterministic automata. * How to get the regular expression from an automaton. * Why two seemingly different regular expressions can belong to the same automaton. * How the regular expression for an infinite automaton is different than one for a finite one. * The relationship of a regular expression to a regular language. * What a generating function for a language tells you about the language. * How to get a generating function from a regular expression. * How the generating function of a recursive regular expression is different from that of an ordinary regular expression. * How to test divisibility properties of integers (binary and decimal based) using automata. * How to construct an automaton to search for a given pattern, or for a given pattern not occurring. * How to construct an automaton for arbitrary patterns and alphabets. * How the recursive regular expression for nested parentheses leads to the Catalan numbers. Included in this book: * Divisibility problems in binary and decimal. * Pattern search problems in binary, ternary, and quaternary alphabets. * Pattern search problems for circular strings that contain or do not contain a given pattern. * Automata, regular expressions, and generating functions for gambling games. * Automata and generating functions for finite and infinite correctly nested parentheses. * The recursive regular expression for matching regular expressions over a binary alphabet. * A further reading list.

In 1956, a physicist named John Kelly working at Bell Labs published a paper titled "A New Interpretation of Information Rate." In the paper he draws an analogy between the outcomes of a gambling game and the transmission of symbols over a communications channel. For a positive expectation game, Kelly showed that a betting system based on a fixed fraction of the bankroll can make the bankroll grow at an exponential rate in the long run. The exponential growth rate in this case is directly analogous to the rate of information transmission through a communications channel. This book examines the Kelly system in detail. Applications of the Kelly system in both gambling and investing are considered. Python code for calculating the Kelly fractions for both a single stock investment and an investment in two stocks simultaneously is included. Included is an introductory review chapter on the probability theory needed to analyze gambling systems in general.There is also a chapter on some of the more commonly used gambling systems such as the Martingale system. This book will be useful for anyone interested in a good mathematical introduction to gambling systems in general, and the Kelly system in particular.

The discovery of nuclear magnetic resonance earned Felix Bloch and Ed Purcell the 1952 Nobel Prize in Physics. What their discovery took advantage of, is that protons are the world's smallest magnets. These tiny magnets can also be used to make a magnetometer, of the type described in this book. This book describes how to build a proton precession magnetometer, suitable for measurements of the Earth's magnetic field. This method of measuring magnetic fields offers the theoretically highest possible precision, limited only by the known value of the gyromagnetic ratio of the proton. Uses of the magnetometer include: making precise measurements of the Earth's magnetic field, calibrating low field magnetometers, teaching modern signal processing techniques, demonstrating nuclear magnetism and NMR to students, and measuring nuclear magnetic relaxation in liquids. The Earth's field proton precession magnetometer, called the Magnum, described in this book, was formerly a commercial product, developed and sold by Exstrom Laboratories LLC. It was designed by Stefan Hollos and Richard Hollos.