Math Circles Meeting on December 5th, 2015

Agenda: Fractal Dimensions

Presenters: Aubrey Rhoden and Kim Moore

Understanding Fractal Dimensions

More Fractal Dimensions

Exploring Fractal Dimensions Student Worksheet

Sierpinski Triangle

  • What patterns are there in the Sierpinski Triangle?
  • What is the rule for the number of shaded triangles in n iterations?
  • What is the rule for the number of unshaded triangles in n iterations?
  • What fraction of the triangles are shaded in n iterations?
  • How do you describe the dimension of a Sierpinski Triangle?

Sierpinski Carpet

  • What patterns are there in the Sierpinski Carpet?
  • What is the rule for the number of shaded squares in n iterations?
  • What is the rule for the number of unshaded squares in n iterations?
  • What fraction of the squares are shaded in n iterations?
  • How do you describe the dimension of a Sierpinski Carpet?

Koch Snowflake

How do you describe the dimensions of a Koch Snowflake?

tetrahedronHow do you describe the dimension of a Sierpinski Tetrahedron?

Menger Sponge

How do you describe the dimensions of a Menger Sponge?

Making the Tree

Koch Snowflake Template

Sierpinski Tetrahedron Template

Menger Sponge Template

fractal Christmas tree

 

 

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