Cynthia Lanius

    Why Study Fractals?

 
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

  Awards
    This Site has received

 


What's so hot about fractals, anyway?

They're New!

Most math you study in school is old knowledge. For example, the geometry you study about circles, squares, and triangles was organized around 300 B.C. by a man named Euclid. Much of fractal geometry, however, is much newer. Research on fractals is being carried out right now by mathematicians. Have you ever thought about a career as a mathematician?

You can understand them.

Much research in mathematics is currently being done all over the world. Most of it is extremely complicated. Although we need to study and learn more before we can understand most modern mathematics, there's a lot about fractals that we can understand.

Objects in nature often look fractal in structure.

Most objects in nature aren't formed of squares or triangles, but of more complicated geometric figures. Many natural objects - ferns, coastlines, etc. - are shaped like fractals. Here you can read about fractals in nature.

There are some really cool concepts connected to fractals.

Imagine that the picture at the top of this page is a picture of the coastline of Africa.You measure it with mile-long rulers and get a certain measurement. What if on the next day you measure it with foot-long rulers? Which measurement would give you a larger measurement. Since the coastline is jagged, you could get into the nooks and crannies better with the foot-long ruler, so it would yield a greater measurement. Now what if you measured it with an inch-long ruler? You could really get into the teeniest and tiniest of crannies there. So the measurement would be even bigger, that is if the coastline is jagged smaller than an inch. What if it were jagged at every point on the coastline? You could measure it with shorter and shorter rulers, and the measurement would get longer and longer. You could even measure it with infinitesimally short rulers, and the coastline would be infinitely long. That's fractal.

People use them to solve real-world problems.

Engineers have begun designing and constructing fractals in order to solve practical engineering problems. For example take a look at Amalgamated Research Ic.'s Fractal Control of Fluid Dynamics.

Internet Research Questions:

You can find the answers from the sites linked above.
  1. Who organized geometry into a series of books? What are those books called?

  2. What is the name of a mathematician who does research today? Where does he/she work? What is the area of mathematics in which he/she works?

  3. Find another picture of a fractal that looks like an object in nature.

If possible, email me your answers.

lanius@math.rice.edu

You may obtain a print version of this page.

. Copyright 1996-2007 Cynthia Lanius
URL http://math.rice.edu/~lanius/fractals/WHY