1 / 11

An introduction to Fractals

An introduction to Fractals. Ginny Bohme Teachers’ Circle March 3, 2011. Why Study Fractals?. Algebra. Geometry. Lungs. Nature. Neurons. Fractals Are SMART: Science, Math & Art! www.FractalFoundation.org. Characteristics of Fractals. Self Similarity Seed~ initiator

elmo-wyatt
Download Presentation

An introduction to Fractals

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. An introduction to Fractals Ginny Bohme Teachers’ Circle March 3, 2011

  2. Why Study Fractals? Algebra Geometry Lungs Nature Neurons Fractals Are SMART: Science, Math & Art! www.FractalFoundation.org

  3. Characteristics of Fractals • Self Similarity • Seed~ initiator • Iterative Process~ rule

  4. Single Iteration ActivityThanks to Evan Maletsky • Seed- Equilateral Triangle • Iterative Process- Fold the top vertex to the midpoint of the opposite side, Then unfold.

  5. 2010 Common Core Standards for Mathematical Practice • Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. • Look for and express regularity in repeated reasoning.

  6. 1 unit 1 unit 1 unit Lengths in Triangles

  7. Group Explorations • Biome Tree • ***Sierpinski Triangle • Sierpinski Carpet • Koch Snowflake

  8. Fractal Cuts

  9. The Mandelbrot Set Wikipediazn+1 = zn2 + c

  10. Benoît Mandelbrot1924- 2010 Over nearly seven decades, working with dozens of scientists, Dr. Mandelbrot contributed to the fields of geology, medicine, cosmology and engineering. He used the geometry of fractals to explain how galaxies cluster, how wheat prices change over time and how mammalian brains fold as they grow, among other phenomena. http://www.nytimes.com/2010/10/17/us/17mandelbrot.html Complex Analytic Dynamics: Pierre Fatou (1878-1929)- iterative and recursive processes Gaton Julia (1893-1978)- iteration of rational functions

  11. Resources • Fractal Pack- educator's guide • Cynthia Lanius Fractal Unit for Middle School

More Related