Fractal Compression and the Jigsaw Property I

We speed up the screening of a computer image compressed as an iterated function system (IFS) of affine transformations w1, . . ., wN . The idea is to avoid applying a given map to a given point if nothing new would be obtained. Let w(x, y) be the result of applying transformation w to pixel coordinates (x, y) then rounding to the nearest integer pair, say (u, v). Then the w-jigsaw pieces w−1(u, v) tile the plane. We develop a foundation of results about such jigsaws based on the coefficients defining the transformations w, and apply them to a collection of 50 IFSs. Much time is indeed saved and the method is to be pursued further.