The first instance of pre-computer fractals was noted by the French mathematician Gaston Julia. He wondered what a complex polynomial function would look like, such as the ones named after him (in the form of z2 + c, where c is a complex constant with real and imaginary parts). The idea behind this formula is that one takes the x and y coordinates of a point z, and plug them into z in the form of x + i*y, where i is the square root of -1, square this number, and then add c, a constant. Then plug the resulting pair of real and imaginary numbers back into z, run the operation again, and keep doing that until the result is greater than some number.
This first edition of this book is a treasure. It was reprinted later, but roughly the second half of the book is missing in that edition, so get one of these older copies if you can. The book offers a variety of interesting folds, ranging from simple to complex. It also has very nice full-color photos of the models.
In 1614, Osaka Castle was Japan's greatest fortification, measuring approximately 2 miles in length with double circuits of walls, 100 feet high. It was guarded by 100,000 samurai, loyal to their master: the head of the Toyotomi clan, Toyotomi Hideyori. The castle was seemingly impenetrable, however the ruling shogun of the age, Tokugawa Ieyasu, was determined to destroy this one last threat to his position as Japan's ultimate ruler. This book explores the complex background of this bitter struggle, as well as the battle experiences of the opposing forces, in a compelling exploration of the conflict that led to the eventual triumph of one dynasty over another.
Writing is a complex and cognitively demanding activity. To be successful, writers need an understanding of the components of a quality test as well as knowledge of writing strategies that can be used to shape and organise the writing process. This book discusses academic writing as a complex task which involves a variety of cognitive and metacognitive activities; a model for teaching writing strategies and the sociocultural processes of written communication; and, rubric-referenced self-assessment and the quality of elementary and middle-school students' writing and self-efficacy and others.
You could spend years trying to read Walter Benjamin's The Arcades Project--after all, he spent much of the last 13 years of his life doing the research. When he committed suicide in 1940, he destroyed his copy of the manuscript, and so for decades the work was believed lost. But another copy turned up, and Howard Eiland and Kevin McLaughlin have translated it into English. It is a complex, fragmentary work--more a series of notes for a book than a book itself--which probes the culture of the Paris arcades...
