Share Email Print
cover

Proceedings Paper

Fractal transformations of harmonic functions
Author(s): Michael F. Barnsley; Uta Freiberg
Format Member Price Non-Member Price
PDF $17.00 $21.00

Paper Abstract

The theory of fractal homeomorphisms is applied to transform a Sierpinski triangle into what we call a Kigami triangle. The latter is such that the corresponding harmonic functions and the corresponding Laplacian Δ take a relatively simple form. This provides an alternative approach to recent results of Teplyaev. Using a second fractal homeomorphism we prove that the outer boundary of the Kigami triangle possesses a continuous first derivative at every point. This paper shows that IFS theory and the chaos game algorithm provide important tools for analysis on fractals.

Paper Details

Date Published: 3 January 2007
PDF: 12 pages
Proc. SPIE 6417, Complexity and Nonlinear Dynamics, 64170C (3 January 2007); doi: 10.1117/12.696052
Show Author Affiliations
Michael F. Barnsley, The Australian National Univ. (Australia)
Uta Freiberg, The Australian National Univ. (Australia)


Published in SPIE Proceedings Vol. 6417:
Complexity and Nonlinear Dynamics
Axel Bender, Editor(s)

© SPIE. Terms of Use
Back to Top
PREMIUM CONTENT
Sign in to read the full article
Create a free SPIE account to get access to
premium articles and original research
Forgot your username?
close_icon_gray