Dilation (metric space)
In mathematics, a dilation is a function f {\displaystyle f} from a metric space M {\displaystyle M} into itself that satisfies the identity d ( f ( x ) , f ( y ) ) = r d ( x , y ) {\displaystyle d(f(x),f(y))=rd(x,y)} for all points x , y ∈ M {\displaystyle x,y\in M} , where d ( x , y ) {\displaystyle d(x,y)} is the distance from x {\displaystyle x} to y {\displaystyle y} and r {\displaystyle r} is some positive real number. In Euclidean space, such a dilation is a similarity of the space.