is the intersection point of these two quarters of circles. In general metric spaces In a general metric space , an exact similitude is a function from the metric space into itself that multiplies all distances by the same positive scalar , called 's contraction factor, so that for any two points and we have Weaker versions of similarity would for instance have be a bi-Lipschitz function and the scalar a limit This weaker version applies when the metric is an effective resistance on a topologically self-similar set. A self-similar subset of a metric space is a set for which there exists a finite set of similitudes with contraction factors such that is the unique compact subset of for which ] These self-similar sets have a self-similar measure with dimension given by the formula which is often (but not always) equal to the set's Hausdorff dimension and packing dimension. If the overlaps between the are "small", we have the following simple formula for the measure: Topology In topology, a metric space can be constructed by defining a similarity instead of a distance. The similarity is a function such that its value is greater when two points are closer (contrary to the distance, which is a measure of dissimilarity: the closer the points, the lesser the distance). The definition of the similarity can vary among authors, depending on which properties are desired. The basic common properties are Positive defined: Majored by the similarity of one element on itself (auto-similarity): More properties can be invoked, such as reflectivity () or finiteness (). The upper value is often set at 1 (creating a possibility for a probabilistic interpretation of the similitude). Note that, in the topological sense used here, a similarity is a kind of measure. This usage is not the same as the similarity transformation of the and sections of this article. Self-similarity Self-similarity means that a pattern is non-trivially similar to itself, e.g., the set of numbers of the form where ranges over all integers. When this set is plotted on a logarithmic scale it has one-dimensional translational symmetry: adding or subtracting the logarithm of two to the logarithm of one of these numbers produces the logarithm of another of these numbers. In the given set of numbers themselves, this corresponds to a similarity transformation in which the numbers are multiplied or divided by two. Psychology The intuition for the notion