## Why Study Fractals?

Why study fractals?
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

My fractals mail
Send fractals mail

Fractals on the Web
The Math Forum

Other Math Lessons
by Cynthia Lanius

Awards

### 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.