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Lesson Plan Image

Fascinating Fractals

Students will learn about never-ending patterns found in nature and create artwork featuring fractals.

Lesson Plan

Supplies Needed

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  • Paper

Steps

  • Step 1

    A fractal is a never-ending pattern that repeats itself in different scales. Have students think of examples of fractals found in nature, such as trees (the trunk produces branches which are essentially smaller trunks, and branches produce more branches), pinecones (whose spiral design repeats over and over), foam produced by soap (large bubbles are interspersed with smaller bubbles), etc. There are also geometric fractals. For example, a triangle can be broken down into various sizes of other triangles. There are also algebraic fractals that students could research after they have explored more basic examples.

  • Step 2

    Have students create a piece of artwork inspired by a fractal image. They might choose to base the art on a fractal occurring in nature or create their own design using a self-repeating design that gets smaller or larger.

  • Step 3

    Display the students' creations. Have them observe the many artistic ways this mathematical concept can be depicted.

Standards

MATH: Analyze, compare, create, and compose math ideas using written, oral, and drawn lines, shapes, forms, and patterns.

MATH: Look for and create constructed or natural structures and patterns.

Adaptations

Have students investigate practical applications of fractals. For example, since human blood vessels typically grow in an orderly fractal pattern, cancer cells - which grow in an abnormal fashion - are easier to detect. Fractal mathematics has also helped produce realistic computer graphics and computer compression systems.

The term "fractals" was coined in the 1980s by mathematician Benoit Mandelbrot. Have students learn about how he pioneered fractal mathematics and the related chaos theory field. Find out how he used this math to describe - and even predict - stock market trends.