A figure or quantity that is self-similar at all scales. In other word, if under a microscope, the pattern appears similar no matter what the level of magnification. The appearance need not be exact, but merely similar in outline or shape. If a quantity, when plotted on a log-log scale, a straight line would appear. The slope of this line is called the fractal dimension. A usual example is the coastline paradox. Imagine trying to measure the coastline of a country with a ruler: the shorter the ruler, the longer will be the estimate of the length of the coastline. A figure or quantity that is self-similar at all scales. In other word, if under a microscope, the pattern appears similar no matter what the level of magnification. The appearance need not be exact, but merely similar in outline or shape. If a quantity, when plotted on a log-log scale, a straught line would appear. The slope of this line is called the fractal dimension. A usual example is the coastline paradox. Imagine trying to measure the coastline of a country with a ruler: the shorter the ruler, the longer will be the estimate of the length of the coastline.
