2011/02/15 by Michael F. Barnsley, Barnsley, Michael F., Brendan Harding +3
Computer Science · Mathematics · #Cellular Automata and Applications #Computability, Logic, AI Algorithms #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.1102.3199
openalex publication_date 2011/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves fractal geometry, chaotic dynamics, and an interplay between discrete and continuous representations. The underlying mathematics is established and applications to digital imaging are described and exemplified.