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.

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 li

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.

The return of the Strange Attractor Journal, offering a characteristically eclectic collection of high weirdness from the margins of culture. After seven years of silence, the acclaimed Strange Attractor Journal returns with a characteristically eclectic collection of high weirdness from the margins of culture. Covering previously uncharted regions of history, anthropology, art, literature, architecture, science, and magic since 2004, each Journal has presented new and unprecedented research into areas that scholarship has all too often ignored. Featuring essays from academics, artists, enthusiasts, and sorcerers, Journal Five explores matters including the folklore of foghorns; the occult origins of the dissident surrealist secret society the Acéphale; the pleasures of heathen falconry; the dark cosmological mysteries of Bremen's Haus Atlantis; a provisional taxonomy of animals with human faces; a twentieth-century crucifixion on Hampstead Heath, and an unpublished horror script by David MacGillivray and Ken Hollings. Journal Five sees Strange Attractor continuing in its mission to celebrate unpopular culture. Join us. Contributors Nadia Choucha, William Fowler, Jeremy Harte, Ken Hollings, Christopher Josiffe, Phil Legard, David MacGillivray, Karen Russo, Robert J. Wallis, Dan Wilson, E. H. Wormwood

A heavily expanded edition of Joe Mellen's legendary, long out-of-print auto-trepanation memoir. A heavily expanded edition of Joe Mellen's legendary, long out-of-print auto-trepanation memoir, Bore Hole takes us deep into the dawning of the UK's psychedelic counter culture, and into a mind breaking free from the confines of a traditional English upbringing. Travelling to Morocco and Ibiza, then back to the first spring of swinging London, Joe Mellen discovers the pleasures of hashish, is captivated by the visionary intensity of LSD and, after meeting the Dutch psychedelic guru Bart Huges, attempts the ultimate head trip, the bore hole. As well as a selection of unseen archive photographs, this edition includes a new postscript, essays, appendices and a 1967 interview with Bart Huges.

The goal of these notes is to give a reasonahly com plete, although not exhaustive, discussion of what is commonly referred to as the Hopf bifurcation with applications to spe cific problems, including stability calculations. Historical ly, the subject had its origins in the works of Poincare [1] around 1892 and was extensively discussed by Andronov and Witt [1] and their co-workers starting around 1930. Hopf's basic paper [1] appeared in 1942. Although the term "Poincare Andronov-Hopf bifurcation" is more accurate (sometimes Friedrichs is also included), the name "Hopf Bifurcation" seems more common, so we have used it. Hopf's crucial contribution was the extension from two dimensions to higher dimensions. The principal technique employed in the body of the text is that of invariant manifolds. The method of Ruelle Takens [1] is followed, with details, examples and proofs added. Several parts of the exposition in the main text come from papers of P. Chernoff, J. Dorroh, O. Lanford and F. Weissler to whom we are grateful. The general method of invariant manifolds is common in dynamical systems and in ordinary differential equations: see for example, Hale [1,2] and Hartman [1]. Of course, other methods are also available. In an attempt to keep the picture balanced, we have included samples of alternative approaches. Specifically, we have included a translation (by L. Howard and N. Kopell) of Hopf's original (and generally unavailable) paper.

An exhaustive investigation of the case of Gef, a “talking mongoose” or “man-weasel,” who appeared to a family living on the Isle of Man. “I am the fifth dimension! I am the eighth wonder of the world!” During the mid-1930s, British and overseas newspapers were full of incredible stories about Gef, a “talking mongoose” or “man-weasel” who had allegedly appeared in the home of the Irvings, a farming family in a remote district of the Isle of Man. The creature was said to speak in several languages, to sing, to steal objects from nearby farms, and to eavesdrop on local people. Despite written reports, magazine articles and books, several photographs, fur samples and paw prints, voluminous correspondence, and signed eyewitness statements, there is still no consensus as to what was really happening to the Irving family. Was it a hoax? An extreme case of folie à plusieurs? A poltergeist? The possession of an animal by an evil spirit? Now you can read all the evidence and decide for yourself. Seven years' research and interviews, photographs (many previously unseen), interviews with surviving witnesses, visits to the site—all are presented in this book, the first examination of the case for seventy years. In the words of its mischievous, enigmatic subject, “If you knew what I know, you'd know a hell of a lot!"

The secind installment of the acclaimed new anthology series. Includes 24 articles exploring the outer edges of anthropology, psychology, magick, literature, art, history, science and religion. This journal has become a true product of London's undergound and this new edition opens the gates to a parallel sultural universe that few knew existed a little further.