Cynthia Lanius

How to Make

Small Jurassic Fractal The World's Largest Jurassic Park Fractal

 
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

   
Since you can't make the fractal by paper folding for more than about seven iterations, we are going to use a very important feature of the fractal to create a much larger one starting with the fourth iteration.

Take a look at the real first and second iterations above. Notice the second iteration is made up of two copies of the first.

Now if you inspect the third iteration above, you will see that it is made up of two copies of the second iteration. In fact, every iteration is formed with two copies of the previous one. We are going to use this feature to make further iterations beyond what we can make with paper folding.

Let's start by making a real fourth iteration, what the book calls the first. (Wow, I wish they hadn't done that!)

Follow the directions and make two copies of the book's First Iteration.

See the next step below.

 

 

Tape the two copies together to form the next iteration. It's a puzzle to figure out how you will rotate the copies to make them fit together correctly.

What would you add to that figure to make the iteration below? Try it and email me to let me know you've successfully completed it.
 

Class Project: Have everyone in the class make a First Iteration of the fractal (4 folds). Combine all the fractals to see how large an iteration you can make. Email me your iteration number, and I'll post it on the page. We'll see who can make the World's Largest Jurassic Park Fractal.
Email any questions or comments to
lanius@rice.edu
 
Copyright 1997-2007 Cynthia Lanius
URL http://math.rice.edu/~lanius/frac/world.html