2016/12/02 by Nira Dyn, Dyn, Nira, David Levin +4
Computer Science · Engineering · #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #Computer Graphics and Visualization Techniques #Dynamical Systems (math.DS) #FOS: Mathematics #Image Processing and 3D Reconstruction
paper · pdf · doi:10.48550/arxiv.1612.00630
openalex publication_date 2016/12/02 · openalex created_date 2022/08/31 · openalex updated_date 2026/07/28
Iterated Function Systems (IFSs) have been at the heart of fractal geometry\nalmost from its origin, and several generalizations for the notion of IFS have\nbeen suggested. Subdivision schemes are widely used in computer graphics and\nattempts have been made to link fractals generated by IFSs to limits generated\nby subdivision schemes. With an eye towards establishing connection between\nnon-stationary subdivision schemes and fractals, this paper introduces the\nnotion of "trajectories of maps defined by function systems" which may be\nconsidered as a new generalization of the traditional IFS. The significance and\nthe convergence properties of 'forward' and 'backward' trajectories are\nstudied. In contrast to the ordinary fractals which are self-similar at\ndifferent scales, the attractors of these trajectories may have different\nstructures at different scales.\n