Strange Attractors

Chaos and fractals are new mathematical ideas that have revolutionized our view of the world. They have application in virtually every academic discipline. This book shows examples of the artistic beauty that can arise from very simple equations, and teaches the reader how to produce an endless variety of such patterns. Disk includes a full working version of the program.

This book, based on lectures given at the Accademia dei Lincei, is an accessible and leisurely account of systems that display a chaotic time evolution. This behaviour, though deterministic, has features more characteristic of stochastic systems. The analysis here is based on a statistical technique known as time series analysis and so avoids complex mathematics, yet provides a good understanding of the fundamentals. Professor Ruelle is one of the world's authorities on chaos and dynamical systems and his account here will be welcomed by scientists in physics, engineering, biology, chemistry and economics who encounter nonlinear systems in their research.

Strange Attractors is a collection of approximately 150 poems with strong links to mathematics in content, form, or imagery. The common theme is love, and the editors draw from its various manifestations—romantic love, spiritual love, humorous love, love between parents and children, mathematicians in love, love of mathematics. The poets include literary masters as well as celebrated mathematicians and scientists. "What, after all, is mathematics but the poetry of the mind, and what is poetry but the mathematics of the heart?" So wrote the American mathematician and educator David Eugene Smith. In a similar vein, the German mathematician Karl Weierstrass declared, "A mathematician who is not at the same time something of a poet will never be a full mathematician." Most mathematicians will know what they meant. But what do professional poets think of mathematics? In this delightful collection, the editors present the view of the same terrain—the connections between mathematics and poetry—from the other side of the equation: the poets. Now is your chance to see if the equation balances. —Keith Devlin, mathematician, Stanford University, and author of The Math Gene, The Math Instinct, and The Language of Mathematics

The equations which we are going to study in these notes were first presented in 1963 by E. N. Lorenz. They define a three-dimensional system of ordinary differential equations that depends on three real positive parameters. As we vary the parameters, we change the behaviour of the flow determined by the equations. For some parameter values, numerically computed solutions of the equations oscillate, apparently forever, in the pseudo-random way we now call "chaotic"; this is the main reason for the immense amount of interest generated by the equations in the eighteen years since Lorenz first presented them. In addition, there are some parameter values for which we see "preturbulence", a phenomenon in which trajectories oscillate chaotically for long periods of time before finally settling down to stable stationary or stable periodic behaviour, others in which we see "intermittent chaos", where trajectories alternate be tween chaotic and apparently stable periodic behaviours, and yet others in which we see "noisy periodicity", where trajectories appear chaotic though they stay very close to a non-stable periodic orbit. Though the Lorenz equations were not much studied in the years be tween 1963 and 1975, the number of man, woman, and computer hours spent on them in recent years - since they came to the general attention of mathematicians and other researchers - must be truly immense.

Final issue! Brilliant mathematics student Heller Wilson finds his true calling when he starts connecting with his fellow New Yorkers in a daring attempt to save New York City from a series of catastrophic events.

An award-winning poet living in Prague, Armand presents a collection of his work that pursues the complex challenges language poses.

Shipworld! For John Bandicut, Earth is but a memory. Stranded at the edge of the galaxy in a structure populated with beings from a thousand worlds, Bandicut finds unexpected friends—only to be caught up in a cascade of forces that threaten the Shipworld itself. Confronting an entity known as the boojum, Bandicut discovers greater peril than ever in his journey into the unknown. Volume 2 of The Chaos Chronicles, from the Nebula-nominated author of Eternity’s End. Original print publication by Tor Books. REVIEWS: “A dazzling, thrilling, innovative space opera…probably Carver’s best effort to date.” —Kirkus Reviews “An irresistibly readable story line reinforced by fascinating speculative science. Readers who come this far will be hooked for the series’ duration.” —Booklist “Carver’s latest novel showcases his own fertile imagination and his talent for creating a host of engagingly sympathetic characters.” —Library Journal “Carver is at his rousing best in this wild ride into the heart of an enigmatic world beyond the Milky Way. This is science fiction out at the frontier. Maybe beyond the frontier.” —Jack McDevitt