The First Fractals

 

Benoit Mandelbrot was one of the first to discover fractals. Madelbrot was examining the shapes created by a Gaston Julia, a mathematician in the 1920's who was working without the benefit of computers. Julia could not describe these shapes using Euclidean geometry. His work was obscure and largely forgotten. The image in this text is one of the shapes discovered by Julia. Others looked like pinched circles, some like brambles, some like spots of dust. Mandelbrot tried to classify these shapes. By iterating a simple equation and mapping this equation in the complex plane, Madelbrot discovered the fractal you see at the top of this page. This discovery lead to further information about Julia Sets and fractional dimensions. Find out more by clicking on "Mandelbrot Information" . Compare the Mandelbrot Set to the Julia Sets by clicking on "Julia Sets".

Activities:

• Create a Fractal: using FracInt, a downloadable program, create a fractal.
• Create Musical Fractals: using recursion programs to create the sound of fractals.
• The Fractal Microscope: an interactive tool for examining the Mandelbrot Set. The site includes text on fractals and the Mandelbrot set, as well as a bibliography.
• Studying Mandelbrot Fractals:activity to create and study the Mandelbrot Set and links to supplemental sites

Fractal Generators:

Programs you may download to create fractals

• Fractal Domains: explains generators and provides programs for PC's and Mac's
• The Fractory:interactive site on creating and understanding fractals.
• The King's Dream:downloadable program to create a simple fractal. Good introduction to creating fractals.
• A Fractal Experience:An instructional fractal generator program which was Written by a student. Not available for Macs. Appropriate for Algebra 1 students and above.
• Dynamical Systems and Technology Project:create animated fractals.