Fractal. A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all scales, but the same type of structures must appear on all scales.A plot of the quantity on a log-log graph versus scale then gives a straight line, whose slope is said to be the fractal dimension. fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales.