Cynthia Lanius

  Watch it grow complex!

 
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

   
Here's another look at the fractal after 4 paper-folds, what the book calls the First Iteration.  

 

 

What would the fractal look like after another paper-fold? Let's try it and see.

Take the fractal you made and fold it back together as before, then fold once more, five times in all. Unfold and compare to the Second Iteration below.

If you folded the paper again, it would look like this:

If you could fold the paper again, it would look like this:

If you could fold the paper about 50 times, it would look like this:

But of course, you can't fold the paper 50 times, so you let the computer take over the paper-folding process. A computer can't fold paper!?! No, but it can simulate the process.

Next: Look at the real first iteration.

Download software that creates fractals by simulating the paper-folding process.

lanius@math.rice.edu
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. Copyright 1996-2007 Cynthia Lanius

URL http://math.rice.edu/~lanius/frac/jurr2.html