fractals : intro page

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Fractals
	•	Introduction

General Fractals
	•	Fractals By Replacement
	•	Fractals in Crystals
	•	Natural Fractals Activity

Bifurcations and Branching
	•	The Shortest Distance between 91 points
	•	Branching Networks

Hausdorf dimension
	•	Rocks as Fractals
	•	The Dimension of Shorelines

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The subject of fractals has garnered much public attention lately, and this chapter attempts to explain why. Fractals not only are frequently beautiful, but they also provide useful models for describing many natural phenomena.

The "General Fractals" section provides an introduction to what fractals are. The "Fractals by Replacement" Activity describes how to create fractals by hand; the "Fractals in Crystals" and "Natural Fractals" Activity show naturally occuring examples, and encourage the students to re-create the natural versions by hand and on the computer.

The "Bifurcations and Branching" section considers the question, "why fractals?" Why does a tree (or a river system, or a circulatory system) branch in a fractal pattern instead of (say) a rayed pattern such as airlines use for their routes, or in a winding pattern such as ivy uses?

Finally, the "Hausdorf dimension" section looks at a mathematical measure of the dimension -- that is, the crinkliness -- of various fractals.

Further Reading (etc.): [Ch] Chaos, the New Science [video], New Dimension Media, Inc., Eugene OR (1990). [K] Jay Kappraff, "The Geometry of Coastlines: A study in fractals", Comp. & Maths. with Appls, 12B, nos. 3/4 (1986) pp. 655-671. [M] Dana Mackenzie, "Rocks as Fractals", Physical Review Focus of the American Physical Society, <http://focus.aps.org/v3/st22.html> (Apr. 15, 1999). [Ma] Benoit Mandelbrot, "How long is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension", Science, 156, no. 5. (1967) pp. 636-638. [PG] Eliot Porter and James Gleick, Nature's Chaos, Viking Penguin Books, USA (1990).