Self-similar fractal sets: theory and procedure

Self-similar fractal sets: theory and procedure

The presented algorithm generates approximations of self-similar fractal sets. The algorithm is based on a pattern rewriting system that draws a geometric pattern repeatedly after suitable mappings. A program developed from the algorithm reproduces Mandelbrot's self-similar fractals. We begin b...

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Veröffentlicht in:IEEE computer graphics and applications 1994-05, Vol.14 (3), p.73-82
Hauptverfasser: Casey, S.D., Reingold, N.F.
Format: Magazinearticle
Sprache:eng
Schlagworte:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Bibliographies
Calculus
Collaboration
Computer science
control theory
systems
Encoding
Exact sciences and technology
Fractals
Geometry
Mathematics
Set theory
Theoretical computing
Topology
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Zusammenfassung:The presented algorithm generates approximations of self-similar fractal sets. The algorithm is based on a pattern rewriting system that draws a geometric pattern repeatedly after suitable mappings. A program developed from the algorithm reproduces Mandelbrot's self-similar fractals. We begin by discussing fractals and dimension theory, then present the algorithm, and conclude by using fractal set theory to calculate the dimensions of self-similar sets from their generators.< >
ISSN:0272-1716
1558-1756
DOI:10.1109/38.279048