Cynthia Lanius

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

  Original Triangle
  First Iteration
  Second Iteration

Once more...     Third Iteration

 
And one more time...
  Fourth Iteration

 

 
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.

Copyright 1998-2007 Cynthia Lanius