Information

Abstract

The basic requirement for the functions of an Iterated Function System (IFS for short) is contractivity. Nevertheless the majority of recent scientific investigations is concentrating on IFSs defined through a set of contractive linear functions. Simpler handling of this kind of functions and a more predictable result is the main reason for this approach. In this work we use distorted grids (representing nonlinear functions) to specify an IFS with a higher degree of flexibility and a higher modelling capability. A program for modeling these grids with so-called high-level operations is presented. Attention is directed to the interactivity of designing the IFS and rendering its limit set. Therefore a z-Buffer for displaying the result of a stochastic algorithm is included. Example images designed with the implemented software system are presented.

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BibTeX

@techreport{Groeller-1994-IDN,
  title =      "Interactive Design of Nonlinear Functions for               
                Iterated Function Systems",
  author =     "Meister Eduard Gr{"o}ller and Rainer Wegenkittl",
  year =       "1994",
  abstract =   "The basic requirement for the functions of an Iterated
               Function System (IFS for short) is contractivity.
               Nevertheless the majority of recent scientific
               investigations is concentrating on IFSs defined through a
               set of contractive linear functions. Simpler handling of
               this kind of functions and a more predictable result is the
               main reason for this approach. In this work we use distorted
               grids (representing nonlinear functions) to specify an IFS
               with a higher degree of flexibility and a higher modelling
               capability. A program for modeling these grids with
               so-called high-level operations is presented. Attention is
               directed to the interactivity of designing the IFS and
               rendering its limit set. Therefore a z-Buffer for displaying
               the result of a stochastic algorithm is included. Example
               images designed with the implemented 		software system are
               presented.",
  month =      aug,
  number =     "TR-186-2-94-3",
  address =    "Favoritenstrasse 9-11/186, A-1040 Vienna, Austria",
  institution = "Institute of Computer Graphics and Algorithms, Vienna
               University of Technology",
  note =       "human contact: technical-report@cg.tuwien.ac.at",
  keywords =   "iterated function system (IFS), nonlinear, interactive
               design, fractals, rendering",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/1994/Groeller-1994-IDN/",
}