Name
Abstract | ||
|---|---|---|
Self-affinity and self-similarity are fundamental concepts in fractal geometry. In this paper, they are related to collage grammars — syntactic devices based on hyperedge replacement that generate sets of collages. Essentially, a collage is a picture consisting of geometric parts like line segments, circles, polygons, polyhedra, etc. The overlay of all collages in a collage language yields a fractal pattern. We show that collage grammars of a special type — so-called increasing generalized Sierpinski grammars — yield self-affine fractals. If one replaces the overlay by an intersection of all generated collages, the same result holds for decreasing generalized Sierpinski grammars. Here, the converse also holds: Every self-affine fractal can be generated by a decreasing generalized Sierpinski grammar, which provides a characterization of this class of fractals. |
Year | DOI | Venue |
|---|---|---|
1993 | 10.1016/0304-3975(94)00118-3 | Theoretical Computer Science |
Keywords | DocType | Volume |
generating self-affine fractals,collage grammar | Conference | 145 |
Issue | ISSN | Citations |
1-2 | Theoretical Computer Science | 8 |
PageRank | References | Authors |
0.92 | 9 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| F. Drewes | 1 | 104 | 6.85 |
| Annegret Habel | 2 | 234 | 23.18 |
| Hans-jörg Kreowski | 3 | 298 | 37.05 |
| stefan taubenberger | 4 | 8 | 0.92 |