Title :
Self-similar fractal sets: theory and procedure
Author :
Casey, Stephen D. ; Reingold, Nicholas F.
Author_Institution :
Dept. of Math. & Stat., American Univ., Washington, DC, USA
fDate :
5/1/1994 12:00:00 AM
Abstract :
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.<>
Keywords :
computational geometry; computer graphics; fractals; Mandelbrot´s set; dimension theory; fractal set theory; generators; geometric pattern; mappings; pattern rewriting system; self-similar fractal sets; Bibliographies; Books; Calculus; Collaboration; Encoding; Fractals; Geometry; Mathematics; Set theory; Topology;
Journal_Title :
Computer Graphics and Applications, IEEE
