na broad sense Design Science is the grammar of a language of images Irather than of words. Modern communication techniques enable us to transmit and reconstitute images without needing to know a specific verbal sequence language such as the Morse code or Hungarian. International traffic signs use international image symbols which are not specific to any particular verbal language. An image language differs from a verbal one in that the latter uses a linear string of symbols, whereas the former is multi dimensional. Architectural renderings commonly show projections onto three mutual ly perpendicular planes, or consist of cross sections at different altitudes capa ble of being stacked and representing different floor plans. Such renderings make it difficult to imagine buildings comprising ramps and other features which disguise the separation between floors, and consequently limit the cre ative process of the architect. Analogously, we tend to analyze natural struc tures as if nature had used similar stacked renderings, rather than, for instance, a system of packed spheres, with the result that we fail to perceive the system of organization determining the form of such structures. Perception is a complex process. Our senses record; they are analogous to audio or video devices. We cannot, however, claim that such devices perceive.

The Desktop Fractal Design Handbook is a four-chapter introductory text to fractal geometry. The underlying algorithms are derived from mathematics, which is reflected in the images they produce. Chapter 1 provides an overview of the products of the desktop fractal design system. Chapter 2 describes the installation and operation of hardware and operating system of the design system, along with its maintenance. Chapter 3 outlines the use of the desktop fractal design system, specifically on hot to design fractals on the fractal design screen, maps, paintings, and help screens. Chapter 4 focuses on the many practical applications of fractals. This book will be of value to mathematicians, engineers, graphic artists, teachers, and students.

"Where most books on fractals concentrate on mathematical theory, Alt. Fractals takes a graphical approach. starting with the fractal "standards"--The Sierpinski Triangle and Pyramid, Menger Sponge, Julia Mandelbrot sets - Alt. Fractals explores the world of variations one step removed from the usual textbook versions."--Back cover.

This in-depth look at Fractal Design Painter covers the tools, features and functions of the program''s l atest version as well as providing a host of hints and tips. The CD-ROM includes demo versions for both Mac and Windows 95, and a gallery of images '

An in-depth survey of the design and REALIZATIONS of miniaturized fractal microwave and RF filters Engineers are continually searching for design methods that can satisfy the ever-increasing demand for miniaturization, accuracy, reliability, and fast development time. Design and Realizations of Miniaturized Fractal RF and Microwave Filters provides RF and microwave engineers and researchers, advanced graduate students, and wireless and telecommunication engineers with the knowledge and skills to design and realize miniaturized fractal microwave and RF filters. This book is an essential resource for the realization of portable and cellular phones, WiFi, 3G and 4G, and satellite networks. The text focuses on the synthesis and fabrication of miniaturized fractal filters with symmetrical and asymmetrical frequency characteristics in the C, X and Ku bands, though applications to other frequency bands are considered. Readers will find helpful guidance on: Miniaturized filters in bilevel fashion Simplified methods for the synthesis of pseudo-elliptic electrical networks Methods for extracting coupling coefficients and external quality factors from simulations of the RF/microwave structure Methods for matching theoretical couplings to couplings of structure Including studies of the real-world performance of fractal resonators and sensitivity analyses of suspended substrate realizations, this is a definitive resource for both practicing engineers and students who need timely insight on fractal resonators for compact and low-power microwave and RF applications.

The Fractal Cosmos Calendar has been the most successful calendar for Amber Lotus. Over the years, Amber Lotus has published the development in Fractal Art. Now, Amber Lotus publishes FRactal Images by Lifesmith, including an introductory text, a brief history as well as the mechanics of mathematical art. The book includes 350 color images of popular designs in modern fractals. Amber Lotus also publishes Fractal Arts as greeting cards, wrapping paper, calendars, and blank journals.

From seashells to crystals and clouds, nature abounds in the intricate patterns known as fractals. Thirty-one full-page fractal designs feature kaleidoscopic arrays of flowers, butterflies, and other natural forms.