Hierarchical fixed-point searching method for resizing binary fractal image with IFS code modification

Abstract

Iterated function system's (IFSs) can achieve a very high compression ratio for a fractal image. It iteratively generates a fractal image by the use of, for example, the random iteration algorithm. However, the original sizes and coordinates of fractal images are usually different and they can be measured only from the decoded results. This is a drawback since the decoded fractal image shown on a display of fixed size may not be with an adequate scale and located in a desired position. It should make each decoded fractal image which can be generated with a desired size. In this paper, we propose a fixed-point-searching algorithm which can automatically determine the original size and the coordinates of a fractal image directly from its IFS code. With the proposed modification on the translation parameters in IFS code, we can resize and relocate the decoded image to become a desired one. The computation load is low because only the calculation of certain fixed points are required. Finally, the computer simulation for the fractal fern is performed to demonstrate the decoded fractal image can be displayed with a desired size.