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Page 46

		1.4.1— Dimension: A Quantitative Measure of Self-Similarity and Scaling

		The dimension gives a quantitative measure of the fractal properties of self-similarity and scaling.

		The dimension tells us how many additional smaller pieces of an object are revealed when it is magnified by a certain amount.

		There are a number of different dimensions. Each dimension measures different properties of an object. They can be grouped into three different types of dimensions:

		1— Fractal Dimension

		The fractal dimension describes how an object fills up space.

		It gives us information about the length, area, or volume of an object.

		Its value can be an integer or a fraction (for example: 2 or 1.7).

		2— Topological Dimension

		The topological dimension describes how points within an object are connected to each other.

		It tells us that an object is an edge, a surface, or a solid.

		Its value is always an integer (for example: 1 or 2).

		3— Embedding Dimension

		The embedding dimension describes the space that contains the object.

		It tells us that this space is a line, an area, or a volume.

		Its value can be an integer or a fraction (for example: 2 or 1.7).

 

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