March 2 is Read Across America Day, the annual tribute to the pleasures and importance of reading founded in 1998 by the National Education Association.
Fractals are geometric shapes that repeat themselves, each part of which is a smaller copy of the original shape. The mathematical term applied to this notion is called self-similarity, but to a non-mathematician like me, fractals are like little halls of mirrors, where the shape decreases in size with each reiteration. They are found in abundance in nature, in the patterns of clouds, fern fronds, coastlines, and so forth. They are, in a word, cool.
Fractals are appealing on many levels. Most students are appropriately impressed (at least for the short term) when shown images of how fractals occur in nature, both on earth and in space. Yet when confronted with new or sometimes challenging material, students often ask how such material is relevant to their lives. Aside from creating amazing patterns (and thus used to great effect in various types of art), fractals are in fact are widely used in a host of industries, including engineering, economics, biotechnology, computer science, and entertainment. Fractals, for example, are used in the design of computer networks, most notably in how data traffic patterns are configured. They are also used in data and digital image compression, with the advantage of offering little to no pixilation difficulties that are commonly found in jpeg and gif formats. Microsoft used fractal data compression when it issued its Encarta Encyclopedia, where thousands of articles, color images, and animations were compressed into less than 600 megabytes of data.
The engineering and manufacturing industries also rely on the benefits of fractal geometry. The strength of coiled springs, for example, can be tested in several minutes as opposed to several days as a result of fractal modeling, and agricultural and civil engineers use fractal simulations to determine the best design, layout, and location of pipes and settling tanks related to ground seepage and water filtration. DNA sequences have been determined to show fractal patterns, which has led to new research for applications in biotechnology, and fractal theory, specifically the Mandelbrot set, is widely used in predicting stock market prices. Students may be most interested to learn that fractals are widely used in computer graphics and animations for the film industry. Like those rain droplets running down the dinosaurs’ skins in Jurassic Park? Those were created by using fractal models, as were planet topographies in various Star Wars and Star Trek films, among many others.
This week we have selected resources that offer a variety of lessons and activities on fractals, all products of Shodor Interactivate. A project of the Shodor Education Foundation, Interactivate offers interactive Java-based resources in math and science. All lessons are aligned to a variety of state and national education standards.
This week’s Joann’s Picks column on the Gateway’s home page, www.TheGateway.org, focuses on resources to help your students learn about Fractals. Peggy’s Corner will discuss online tools and providers that can help you tackle this important subject with your students. Additional resources on the topic will be presented and discussed on the Gateway’s Facebook (http://www.facebook.com/TheGateway.org) and Twitter (http://twitter.com/Gatewaytoskills) pages.
Discussions will also continue on last week’s theme of the Russian Revolution on both pages. All of the weekly Gateway columns and resource selections are archived on the following blog site: http://thegatewayto21stcenturyskills.blogspot.com/.
Resources covered in this week’s columns include:
Introduction to Fractals: Geometric Fractals
This lesson outlines the approach to building fractals by cutting out portions of plane figures. Students are also introduced to other classic fractals, such as the Sierpinski Triangle and Carpet as they iterate with plane figures.
In this online activity, students step through the generation of Sierpinski's Carpet – a fractal made by subdividing a square into nine smaller triangles, and then removing the middle square. This activity allows students to explore number patterns in sequences and geometric properties of fractals.
Prisoners and Escapees – Julia Sets
One of the most famous fractals, the Mandelbrot Set, is made up of Julia Sets. Julia Sets, in turn, are known as prisoner sets. This resource provides a brief overview of the notion of prisoners and escapees as they pertain to iterative functions. A prisoner ultimately changes to a constant while escapees iterate to infinity.
About The Gateway to 21st Century Skills
The Gateway has been serving teachers continuously since 1996. It is the oldest publicly accessible U.S. repository of educational resources on the Web and the oldest continuously operating service of its kind in the world. The Gateway is sponsored by the National Education Association (NEA) and supported by over 700 quality contributors. The Gateway to 21st Century Skills is the cornerstone of the Global Learning Resource Connection (GLRC) which is a JES & Co. program.
About Joann Wasik- Author of Joann’s Picks
Joann is the Metadata Cataloger for The Gateway for 21st Century Skills. Her primary responsibilities for The Gateway include locating and cataloging standards-based K-12 lessons and activities for The Gateway, as well as writing the “Joann’s Picks” weekly column. Before joining The Gateway in 2006, Joann had been involved with numerous projects at the Information Institute of Syracuse at Syracuse University, including virtual reference with the Virtual Reference Desk (VRD) project; virtual reference competencies and education with the Digital Reference Education Initiative (DREI) project; and metadata cataloging with the Gateway for Educational Materials (GEM). Her previous experience also includes technology training and positions in academic libraries. She also conducts freelance research for business and educational clients. Joann holds B.A. and M.A.T. degrees in English from Boston College, and an M.L.S. degree from Syracuse University.
About Peggy James- Author of Peggy’s Corner
Peggy received her B.S. in Molecular and Cellular Biology from The University of Arizona, and continued on to earn her M.Ed. from the U of A as well. She has taught Physical Science and Chemistry at the high school level. She is working toward her endorsement in Gifted Education, and has been actively involved in coaching and volunteering in Odyssey of the Mind and Academic Decathlon. She has a passion for teaching critical thinking and creativity in the classroom. She has done work evaluating and aligning lesson plans to standards as a curriculum consultant with the National Education Association Health Information Network. She is very excited to help create a collaborative environment for educators to discover new resources that will enhance their teaching!
About the GLRC
About JES & Co.
JES & Co., a publicly funded 501(c) (3) education research organization, is a leader in research and deployment of education programs based on open standards. With 20 years of experience in interoperability and portability of educational resources, organizations around the world come to JES & Co. for leadership and guidance on education programs and initiatives. Since its establishment in the early 1990s, JES & Co. has led and managed The Achievement Standards Network (ASN), The Partnership for 21st Century Skills, The Gateway to 21st Century Skills (formerly known as GEM), the Dell Academy, the Intel Student Certification Program, and Microsoft’s Partners in Learning. For more information about JES & Co. or the Global Learning Resource Connection, visit www.JESandCo.org.
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