Fractals - Section 3


     3.1  A revolutionary and useful new way of thinking about fractals began about 20 years ago.
     3.2  John Hutchinson
     3.3  Ingredient 1: Contractions
     3.4  an example
     3.5  The Contraction Mapping Theorem
     3.6  Stefan Banach
     3.7  Ingredient 2: Hausdorff distance
     3.8  Felix Hausdorff
     3.9  Sierpinski triangle as a SET fixed by a contraction mapping, where you use Hausdorff distance to measure how far apart sets are.
     3.10  Even if you started with Bob, as you iterated F he would turn into Sierpinski!
     3.11  Hutchinson's Theorem, precisely.
     3.12  Mapping templates and fractal images; some examples from the book "Fractals for the Classroom", by Peitgen, Jurgens, Saupe.
     3.13  Some more examples from their book.
     3.14  More,
     3.15  and more.
     3.16  Creations by our very own University of Utah students,
     3.17  and some more.

     ~korevaar/fractals   A directory with fractal examples, and maple procedures for making them.
     ACCESS2002   back to our home page.