## Information

- Publication Type: Technical Report
- Workgroup(s)/Project(s): not specified
- Date: November 1994
- Number: TR-186-2-94-12
- Keywords: Fractals, Iterated Functions Systems, nonlinear, Modeling, Rendering

## Abstract

Iterated Function Systems are typically defined
through sets of contractive linear transformations.
The theory of Iterated Function Systems is based on
the contractivity but not on the linearity of the
defining functions. Piecewise bilinear distortions
of grids are used in this work to specify nonlinear
Iterated Function Systems. Nonlinear Iterated Functions
Systems are characterized by a higher degree of
flexibility and greater modeling capability than their
linear counterparts. Modeling and rendering aspects are
discussed. Limit sets of 2D nonlinear Iterated Function
Systems are represented by approximating point sets.
Limit sets of 3D nonlinear Iterated Function Systems
are either rendered by displaying approximating point
sets (z-buffer approach) or through ray tracing an
approximate set of 3D solids. Example images of a
test implementation are presented.

## Additional Files and Images

## Weblinks

No further information available.

## BibTeX

@techreport{Groeller-1994-MRN,
title = "Modeling and Rendering of Nonlinear Iterated
Function Systems",
author = "Meister Eduard Gr\"{o}ller",
year = "1994",
abstract = "Iterated Function Systems are typically defined through sets
of contractive linear transformations. The theory of
Iterated Function Systems is based on the contractivity but
not on the linearity of the defining functions. Piecewise
bilinear distortions of grids are used in this work to
specify nonlinear Iterated Function Systems. Nonlinear
Iterated Functions Systems are characterized by a higher
degree of flexibility and greater modeling capability than
their linear counterparts. Modeling and rendering aspects
are discussed. Limit sets of 2D nonlinear Iterated Function
Systems are represented by approximating point sets. Limit
sets of 3D nonlinear Iterated Function Systems are either
rendered by displaying approximating point sets (z-buffer
approach) or through ray tracing an approximate set of 3D
solids. Example images of a test
implementation are presented.",
month = nov,
number = "TR-186-2-94-12",
address = "Favoritenstrasse 9-11/E193-02, 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 = "Fractals, Iterated Functions Systems, nonlinear, Modeling,
Rendering",
URL = "https://www.cg.tuwien.ac.at/research/publications/1994/Groeller-1994-MRN/",
}