Fractal image compression using the iterative function system (IFS) is based on the collage theorem proposed by Barnsley et al. (1986). In this conventional method, the errors between the reconstructed image and original image may be greater than the errors between the collage and original image because the collage theorem does not guarantee the former errors to be smaller than the latter errors. This paper proposes an extended collage theorem. An IFS algorithm based on this theorem determines the parameters after iterations of the contraction mappings. An image reconstructed according to the new theorem has higher quality than one based on the existing collage theorem. The reconstructed image can be gotten by fewer iterations than by the conventional IFS.

A methodology of impurity diffusion in semiconductors by the Monte Carlo method has been presented. The simulation is carried out by repeating the motion of both vacancies and self-interstitials with the complementary weighting factor for the jumps of respective point defects. This method is applied to impurity diffusion from a limited source in a virtual semiconductor crystal and its validity is confirmed.