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Physics

Theses/Dissertations

Fractals

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Full-Text Articles in Physical Sciences and Mathematics

A Fractal Geometry For Hydrodynamics, Jonah Mears Apr 2022

A Fractal Geometry For Hydrodynamics, Jonah Mears

Honors Theses

Experiments have shown that objects with uneven surfaces, such as golf balls, can have less drag than those with smooth surfaces. Since fractal surfaces appear naturally in other areas, it must be asked if they can produce less drag than a traditional surface and save energy. Little or no research has been conducted so far on this question. The purpose of this project is to see if fractal geometry can improve boat hull design by producing a hull with low friction.


The Dimension Of A Chaotic Attractor, Roslyn Gay Lindquist May 1991

The Dimension Of A Chaotic Attractor, Roslyn Gay Lindquist

Dissertations and Theses

Tools to explore chaos are as far away as a personal computer or a pocket calculator. A few lines of simple equations in BASIC produce fantastic graphic displays. In the following computer experiment, the dimension of a strange attractor is found by three algorithms; Shaw's, Grassberger-Procaccia's and Guckenheimer's. The programs were tested on the Henon attractor which has a known fractal dimension. Shaw's and Guckenheimer's algorithms were tested with 1000 data points, and Grassberger's with 100 points, a data set easily handled by a PC in one hour or less using BASIC or any other language restricted to 640K RAM. …


A Fractal Analysis Of Diffusion Limited Aggregation, Cliff Myers Jan 1988

A Fractal Analysis Of Diffusion Limited Aggregation, Cliff Myers

Dissertations and Theses

A modified Witten-Sander algorithm was devised for the diffusion-limited aggregation process. The simulation and analysis were performed on a personal computer. The fractal dimension was determined by using various forms of a two-point density correlation function and by the radius of gyration. The results of computing the correlation function with square and circular windows were analyzed. The correlation function was further modified to include the edge from analysis and those results were compared to the fractal dimensions obtained from the whole aggregate. The fractal dimensions of 1.67 ± .01 and 1.75 ± .08 agree with the accepted values. Animation of …