Escape-time visualization method for language-restricted iterated function systems

The escape-time method was introduced to generate images of Julia and Mandelbrot sets, then applied to visualize attractors of iterated function systems. This paper extends it further to language-restricted iterated function systems (LRIFS’s). They generalize the original definition of IFS’s by providing means for restricting the sequences of applicable transformations. The resulting attractors include sets that cannot be generated using ordinary IFS’s. The concepts of this paper are expressed using the terminology of formal languages and finite automata.

[1]  Heinz-Otto Peitgen,et al.  The science of fractal images , 2011 .

[2]  Dana S. Scott,et al.  Finite Automata and Their Decision Problems , 1959, IBM J. Res. Dev..

[3]  Dietmar Saupe,et al.  Rendering Methods for Iterated Function Systems , 1991 .

[4]  M. Barnsley,et al.  Recurrent iterated function systems , 1989 .

[5]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[6]  Arnaud Jacquin,et al.  Harnessing chaos for image synthesis , 1988, SIGGRAPH.

[7]  Karel Culik,et al.  Affine automata and related techniques for generation of complex images , 1993, Theor. Comput. Sci..

[8]  John C. Hart,et al.  Efficient antialiased rendering of 3-D linear fractals , 1991, SIGGRAPH.

[9]  Marc A. Berger.  Images Generated by Orbits of 2-D Markov Chains , 1989 .

[10]  Michael F. Barnsley,et al.  Fractals everywhere , 1988 .

[11]  E. Vrscay.  Iterated function systems: theory, applications and the inverse problem , 1991 .

[12]  Karel Culik,et al.  Balancing order and chaos in image generation , 1993, Comput. Graph..

[13]  Peter H. Richter,et al.  The Beauty of Fractals , 1988, 1988.

[14]  John Hart,et al.  The object instancing paradigm for linear fractal modeling , 1992 .

[15]  C. Bandt.  Self-similar sets 3. Constructions with sofic systems , 1989 .

[16]  Przemyslaw Prusinkiewicz,et al.  The Algorithmic Beauty of Plants , 1990, The Virtual Laboratory.

[17]  Przemyslaw Prusinkiewcz,et al.  Koch curves as attractors and repellers , 1988, IEEE Computer Graphics and Applications.