MSc Project Presentation: Determining the Language Restrictions of IFS Attractor Subsets (Harrison Tieman)

Abstract: 

This research began with a focus on generating an equivalent Iterated Function System (IFS) to that of a Language-Restricted Iterated Function System (LRIFS) in order for their attractors to be generated deterministically rather than using the randomly oriented chaos game approach. This work allowed for an inverse approach to be utilized in order to determine the language restrictions which were applied to the given IFS to generate its subset attractor approximation. In the comparison between an IFS and its LRIFS subset, these findings can be used for applications such as security measures due to the work’s ability to generate codes of extreme length based on an image of a subset of an IFS attractor approximation.

While the randomly generated attractor approximations of an LRIFS are rich and display underlying common patterns amongst randomness, not having specified unique functions creates difficulties in the analysis of points to a specified iteration. In this transformation from LRIFS to IFS we can now deterministically generate specified iterations upon a starting point rather than being forced to select functions randomly. This improvement allows for an inverse problem to be created such that no possible combination would be missing. This new approach allows us to analyze attractor approximations in order to determine the language restriction in effect.