| fractal | is a kind of geometrical object |  |
| has dimensions fractional | |
| has definition A geometric figure in which a pattern is repeated ad infinitum on smaller and smaller scales. A classic example is Von Koch's snowflake, for which the construction begins with an equilateral triangle. Trisect each side, and replace the middle section by two sides of a smaller equilateral triangle, bulging outward. The snowflake is obtained by repeating this process for each side of the resulting figure, then for each side of the subsequent figure, and continuing forever. | |
| has definition A pattern that repeats itself or nearly repeats itself on many different scales of magnification. For example, suppose that some ink on a piece of paper appears to form a star. If you look at the piece of paper with a magnifying glass, you see that the dark areas are not solid black, but are formed of tiny stars themselves. If you look at one of these small stars with a microscope, you see that the dark areas of each of the tiny stars is formed from an arrangement of even tinier stars. Such a repeating pattern of stars would be called a fractal. | |
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