Cynthia Lanius

Mandelbrot Set     Fractals

Pictured: A Famous Fractal - The Mandelbrot Set

A Fractals Unit for Elementary and Middle School Students

That Adults are Free to Enjoy


Table of Contents

  Why study fractals?
    What's so hot about
    fractals, anyway?

  Making fractals
    Sierpinski Triangle
         Using Java
         Math questions
         Sierpinski Meets Pascal
    Jurassic Park Fractal
         It grows complex
         Real first iteration
         Encoding the Fractal
         World's Largest
    Koch Snowflake
         Infinite perimeter
         Finite area

  Fractal Properties
    Fractional dimension
    Formation by iteration

  For Teachers
    Teachers' Notes

    My fractals mail
    Send fractals mail

  Fractals on the Web
    The Math Forum

  Other Math Lessons
    by Cynthia Lanius


What are Fractals?

They're everywhere, those bright, weird, beautiful shapes called fractals. But what are they, really?

Fractals are geometric figures, just like rectangles, circles and squares, but fractals have special properties that those figures do not have.

There's lots of information on the Web about fractals, but most of it is either just pretty pictures or very high-level mathematics. So this fractals site is for kids, to help them understand what the weird pictures are all about - that it's math - and that it's fun!

Teachers: Every lesson has a print version for classroom use.

Thanks to Sarah Seastone at The Math Forum for her invaluable assistance with editing these pages.

Fractals make "Cool Science" News
4 stars Winners and New Champions!

Congratulations! Students in Mr. Lynch's class in Sandpoint, Idaho created this 11th iteration Jurassic Park Fractal. It took 128 copies of their original to make. Great job.

Elementary School Champions! Third grade students in Ms. Renner's class at Alief ISD's Chambers Elementary in Houston, TX made this this 9th iteration Jurassic Park Fractal. Wow!


Fractals receive recognition: