What Are Fractals?
Isa S. Jubran, Ph.D., SUNY College at Cortland ----------------- e-mail
Lesson Plans and Units on Fractals
- [Lesson Plans on Fractals]: Project Interactivate at Shodor.org has many lesson plans dealing with fractals such as: Introduction to Fractals: Infinity, Self-Similarity and Recursion --- Geometric Fractals
--- Fractals and the Chaos Game --- Properties of Fractals --- Irregular Fractals --- The Mandelbrot Set.
- [ Fractal Geometry]: This site has dozens of labs and lesson plans dealing with fractals. Probably the most comprehenseive site on fractals with lots of information and easy to use software.
- [Pattern Exploration:
Integrating Math and Science
for the Middle School]: This is an excellent site containing over 30 units involving patterns and fractals. Units are complete with blackline masters and answer sheets.
- [A Fractals Unit for Elementary and Middle School Students]: This site has a number of activities and lesson plans mostly for elementary shcool.
- [Special Projects]: This site has a few projects and some excellent information on fractal dimension.
Tutorials on Fractals
- Fractal Geometry, Yale University
- Dynamical Systems and Fractals
- Introduction to Fractal Theory
- Fractals: An Introductory Lesson
- An Introduction to Fractals by Paul Bourke
- Fractals Unleashed
Useful Sites
- [ Fractal Geometry]: This site has a wealth of information on fractals. Of particular interest should be section 13 which contains a
suite of Java Applets illustrating fractal geometry and and chaotic dynamics. Check out the applets Deterministic IFS, Random IFS, Affine Transformation Calculator, Box Counting Dimension and
Mandelbrot and Julia Sets. Sections 11, and 12 have a number of labs and lesson plans on fractals. There is even a Fractal Music Composer applet!
- [IFS Costruction Kit[: This site has an excellent, somewhat easy to use, piece of software which can be used to generate many types of fractals.
- [The Dynamical Systems and Technology Project at Boston University]: This site has many java applets on fractals and chaos and a lot of useful info.
- [JAVA APPLETS for Chaos and Fractals]: This site has a number of useful java applets such as
Chaos Game - Sierpinski Gasket, NSF Pattern Exploration, The Chaos Game, a graphical IFS editor, IFS applet of fern, leaf, etc., Coastline of Hong Kong , and Henon map, Circle map and Sinai Map.
- [The Chaos Hypertextbook]: This site has good information on fractals.
- [Lesson Plans on Fractals]: Project interactivate at Shodor.org.
- [Fractal Maker]: This site by Robert Hasson has a nice java applet for making fractals from iterated function systems. A linear algebra applet to go with the fractal maker can be found at
[Linear Equation Solver]