Exploring the Fascinating World of Fractals

Authors

  • Tippaporn Eungrasamee Department of Mathematics, Faculty of Science, Ramkhamhaeng University

Keywords:

fractals, iterative processes, non-integer dimension, self-similarity

Abstract

Fractals are complex geometric structures defined by self-similarity, infinite detail, and non-integer dimensions. This article introduces the basic properties and formal definition of fractals. The methods for generating fractals through recursive algorithms and iterative functions are discussed with examples such as the Mandelbrot set, Sierpinski triangle, and Koch snowflake.

References

Addison PS (1997) Fractals and Chaos: An Illustrated Course. Institute of Physics. ISBN 0-7503-0400-6

Barnsley MF, Rising H (1993) Fractals Everywhere. Boston: Academic Press Professional. ISBN 0-12-079061-0

Devaney RL (1995) Chaos in the Classroom. Boston University, Boston, MA 02215. https://math.bu.edu/DYSYS/chaos-game/chaos-game.html

Fisher Y (1995) Fractal Image Compression: Theory and Application. Springer

Mandelbrot BB (1982) The Fractal Geometry of Nature. WH Freeman and Company

Ochoa G (1998) An Introduction to Lindenmayer Systems. The University of Sussex. https://www-archiv.fdm.uni-hamburg.de/b-online/e28_3/lsys.html

Peitgen HO, Jurgens H, Saupe D (1992) Chaos and Fractals: New Frontiers of Science. Springer

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Published

2024-12-31

Issue

Section

Review Articles