Fractals Lesson 6-6.

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Presentation transcript:

Fractals Lesson 6-6

WHAT ARE FRACTALS?  A fractal is a figure generated by repeating a special sequence of steps infinitely often.  The patterns are formed by a process known as iteration.  Fractals are self-similar – the smaller details of the figure have the same geometric characteristics of the original form.

FACTS ABOUT FRACTALS  Fractals were discovered in 1975 by Benoît Mandelbrot.  The term is defined from the Latin word fractus, meaning “broken” or “fractured”.  Mathematically, fractals can be generated using a recursive formula.  Fractals can also be found in nature, art, and music.

Let’s Try One!

Stage 0: On the provided grid paper, draw a square with 20 unit sides. Stage 1: Divide the square into 4 congruent squares and shade the top left- hand square. Stage 2: Repeat the process with the three remaining squares. Stage 3 and 4: Repeat the process with the remaining squares.

FRACTAL PROJECTPROJECT

OPTION 1 FRACTALS IN NATURE You will find examples of fractals in nature and everyday items. You will present your findings on a tri-fold poster build. Your poster must include a title, 10 various examples with pictures, and a description of each picture. The description should explain the characteristics of the fractals. The internet will be a great source.

OPTION 2 READ ALL ABOUT IT You are a writer for the magazine Everyday Mathematics for Everyday People. You will write an article describing fractals and why it is important for the public to understand fractals. Pictures must be included within the article and questions will be provided to help in writing the article.

OPTION 3 POWERPOINT PRESENTATION You will create a powerpoint presentation discussing the history of fractals (Benoît Mandelbrot) and the math used in creating fractals. You will need to have at least 16 slides and 7 images.

OPTION 4 LIGHTS, CAMERA, ACTION You and a partner will video tape a newscast on how meteorologists use fractals to predict weather patterns. Your newscast should be at least 3 minutes long. A partner does not that one holds the camera, while the other does the newscast. Both individuals must be on the video.

OPTION 5 FRACTALS You will create one of the following fractals, which directions will be provided.

SIERPINSKI TRIANGLE

KOCH SNOWFLAKE

KOCH ANTI-SNOWFLAKE

SQUARE ITERATION

SQUARE AND ISOSCELES TRIANGLE ITERATION