Fabulous Fractals

“Ed Seeman’s art is alive with myriad shapes that toy with perspective and the figure / ground relationship. A true 1960s sensibility is evident in Ed’s work.” Ed Seeman was a professional artist, photographer and cartoon cel animator for four decades. In 1960s New York, his oil paintings were represented by “East Hampton Galleries” on 57th Street and one of his works was in the New York Metropolitan Museum of Modern Art for three years. Individual paintings have been purchased by the Chrysler Museum in Provincetown, the University of Massachusetts and many private collectors. Five of Seeman’s experimental films are in the US Library of Congress and, most notably, his Frank Zappa and the Mothers of Invention film won a Cine Gold Eagle at the Venice Biennial. His short Space Oddity won a Silver Phoenix at the Atlanta Film Festival. Seeman’s career as a cartoon cel animator began at Paramount Pictures, animating such legendary characters as Popeye and Casper the Friendly Ghost. In TV animation, Seeman brought to the small screen many of the USA’s most popular characters, including My Little Pony. For this work, he has received many Clio awards, Addys and other TV advertising honors. In the process of using computer technology to paint his hand drawn cel animations, Seeman discovered the tremendous digital potential for experimentation in color and abstract form. Thereafter embracing the Giclee method of printing to canvas, he created artistic works from the digital realm that truly reflected the myriad preoccupations of our times. By perfecting his computer painting ability to produce his animated TV commercials, Seeman found he no longer needed to paint with oil and acrylics to produce art on canvas. Now, with the aid of large digital printers, he produces artwork directly from computer to canvas. Colored, pigmented, ultra-violet resistant inks produce much brighter colors than were ever available using ordinary paints. With these technologically enhanced painting tools, Seeman produces uniquely stunning digital abstract artworks. Anthologized herein is a showcase of Seeman’s digital art: over 200 fractals, with an introduction by the artist. These digital artworks were initially emailed individually as .jpeg files by Seeman to a private network of connoisseurs before being formatted into digital e-Book.

Presents twenty activities ideal for an elementary classroom, each of which is divided into sections that summarize the mathematical concept being taught, the skills and knowledge the students will use and gain during the activity, and step-by-step instructions.

Learn about number patterns that exist in a sunflower, the reason behind the hexagonal shape of a honeycomb, and all about the Fibonacci sequence. High impact photographs will draw in young readers as they learn about mathematical concepts they can find outside their front door.

Whether you're hoping to cultivate a calmer mindset, nurture your physical strength or connect with your community, the restorative powers of gardening can help you flourish. With valuable information, actionable tips and creative ideas, this book will help you discover the all-round health benefits that can come while honing your green fingers.

"Curves and Fractals explores curve stitching, a way to approximate a curve using only straight lines; and fractals, which are patterns of shapes that look similar no matter whether you zoon in or out. Build your own fractals such as a Sierpinski triangle and a Koch snowflake. No expensive supplies are required! Everything needed to complete the activities are included or can be found around the house"--

Explores the complexity and wide-ranging applications of the Fibonacci sequence, which appears in nature, art, economics, and the "golden ratio," which is derived from this simple pattern of numbers.

The original title for this work was “Mathematical Literacy, What Is It and Why You Need it”. The current title reflects that there can be no real learning in any subject, unless questions of who, what, when, where, why and how are raised in the minds of the learners. The book is not a mathematical text, and there are no assigned exercises or exams. It is written for reasonably intelligent and curious individuals, both those who value mathematics, aware of its many important applications and others who have been inappropriately exposed to mathematics, leading to indifference to the subject, fear and even loathing. These feelings are all consequences of meaningless presentations, drill, rote learning and being lost as the purpose of what is being studied. Mathematics education needs a radical reform. There is more than one way to accomplish this. Here the author presents his approach of wrapping mathematical ideas in a story. To learn one first must develop an interest in a problem and the curiosity to find how masters of mathematics have solved them. What is necessary to be mathematically literate? It’s not about solving algebraic equations or even making a geometric proof. These are valuable skills but not evidence of literacy. We often seek answers but learning to ask pertinent questions is the road to mathematical literacy. Here is the good news: new mathematical ideas have a way of finding applications. This is known as “the unreasonable effectiveness of mathematics.”

For almost ten years chaos and fractals have been enveloping many areas of mathematics and the natural sciences in their power, creativity and expanse. Reaching far beyond the traditional bounds of mathematics and science to the realms of popular culture, they have captured the attention and enthusiasm of a worldwide audience. The fourteen chapters of the book cover the central ideas and concepts, as well as many related topics including, the Mandelbrot Set, Julia Sets, Cellular Automata, L-Systems, Percolation and Strange Attractors, and each closes with the computer code for a central experiment. In the two appendices, Yuval Fisher discusses the details and ideas of fractal image compression, while Carl J.G. Evertsz and Benoit Mandelbrot introduce the foundations and implications of multifractals.