Title page for ETD etd-042709-134959

Document Type thesis

Author Name Liang, Haodong

Email Address hdliang at wpi.edu

URN etd-042709-134959

Title On the Constructions of Certain Fractal Mixtures

Degree MS

Department Mathematical Sciences

Advisors
Umberto Mosco, Advisor
Bogdan M. Vernescu, Department Head

Keywords
Sierpinski gasket
energy forms
fractal mixture
self-similar

Date of Presentation/Defense 2009-05-01

Availability unrestricted

Abstract
The purpose of this paper is to construct sets, measures and energy forms of certain mixed nested fractals which are spatially homogeneous but not strictly self-similar. We start with the constructions of regular nested fractals, such as Sierpinski gaskets and Koch curves, by employing the iterated map system. Then we show that under the open set condition, the unique invariant (self-similar) measure consists with the normalized Hausdorff measure ristricted on the invariant set. The energy forms construced on regular Sierpinski gaskets and Koch curves is also proved to be a closed form. Next, we use the similar idea, by extending the iterated maps system into a general case, to construct the mixture sets, as well as measures and energy forms. It can be seen that the elements so constructed will not have any strict self-similarity, but them indeed satisfy some weak self-similar properties.

Files
Liang.pdf

Browse by Author | Browse by Department | Search all available ETDs

Questions? Email etd-questions@wpi.edu
Maintained by webmaster@wpi.edu

Document Type	thesis
Author Name	Liang, Haodong
Email Address	hdliang at wpi.edu
URN	etd-042709-134959
Title	On the Constructions of Certain Fractal Mixtures
Degree	MS
Department	Mathematical Sciences
Advisors	Umberto Mosco, Advisor Bogdan M. Vernescu, Department Head
Keywords	Sierpinski gasket energy forms fractal mixture self-similar
Date of Presentation/Defense	2009-05-01
Availability	unrestricted
Abstract The purpose of this paper is to construct sets, measures and energy forms of certain mixed nested fractals which are spatially homogeneous but not strictly self-similar. We start with the constructions of regular nested fractals, such as Sierpinski gaskets and Koch curves, by employing the iterated map system. Then we show that under the open set condition, the unique invariant (self-similar) measure consists with the normalized Hausdorff measure ristricted on the invariant set. The energy forms construced on regular Sierpinski gaskets and Koch curves is also proved to be a closed form. Next, we use the similar idea, by extending the iterated maps system into a general case, to construct the mixture sets, as well as measures and energy forms. It can be seen that the elements so constructed will not have any strict self-similarity, but them indeed satisfy some weak self-similar properties.
Files	Liang.pdf