Cynthia Lanius

 The Anti-Snowflake

 
Table of Contents

   Introduction

  Why study fractals?
    What's so hot about
    fractals, anyway?

  Making fractals
    Sierpinski Triangle
         Using Java
         Math questions
         Sierpinski Meets Pascal
    Jurassic Park Fractal
         Using JAVA
         It grows complex
         Real first iteration
         Encoding the fractal
         World's Largest
    Koch Snowflake
         Using Java
         Infinite perimeter
         Finite area
         Anti-Snowflake
            Using Java

  Fractal Properties
    Self-similarity
    Fractional dimension
    Formation by iteration

  For Teachers
    Teachers' Notes
    Teacher-to-Teacher

  Comments
    My fractals mail
    Send fractals mail

  Fractals on the Web
    The Math Forum

  Other Math Lessons
    by Cynthia Lanius

   
You may print and use this triangle grid paper to help you with the drawing.
 
Let's make another fractal. It's an interesting variation on the Koch Snowflake.

Directions:

Step One. Start with a large equilateral triangle. If you use the triangle grid paper, make the sides of your triangle 9 grid triangles long (or some other multiple of 3).

Step Two. Make a pinwheel:

  1. Divide one side of the triangle into three parts and remove the middle section.

  2. Replace it with two lines the same length as the section you removed, just like in the Koch Snowflake. But this time, instead of turning the section out to form a snowflake, turn them inside the triangle

  3. Do this to all three sides of the triangle.

Step Three. Repeat the process with the "triangles" inside the pinwheel.

 
Want to take a slow and careful look below?

 
Thought Questions:

  1. Compare the perimeter of Anti-Snowflake with that of the Koch Snowflake.
  2. Now compare their areas.

My thanks to William Mcworter, my mathematician caddy, who assists me immeasurably with the mathematics on my pages.

You may obtain a print version of this page.

lanius@math.rice.edu

Copyright 1998-2007 Cynthia Lanius
URL http://math.rice.edu/frac/anti.html