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		1.1.3— The Properties of Fractals

		1— Self-Similarity

		A coastline looks wiggly. You would think that as you enlarge a piece of the coastline the wiggles would be resolved and the coastline would look smooth. But it doesn't. No matter how much you enlarge the coastline it still looks just as wiggly. The coastline is similar to itself at different magnifications. This is called self-similarity.

		2— Scaling

		Because of self-similarity, features at one spatial resolution are related to features at other spatial resolutions. The smaller features are smaller copies of the larger features. The length measured at finer resolution will be longer because it includes these finer features. How the measured properties depend on the resolution used to make the measurement is called the scaling relationship.

		3— Dimension

		The dimension gives a quantitative measure of self-similarity and scaling. It tells us how many new pieces of an object are revealed as it is viewed at higher magnification.

		4— Statistical Properties

		Most likely, the statistics that you were taught in school was limited to the statistics of non-fractal objects. Fractals have different statistical properties that may surprise you!

 

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