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.