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Physical Sciences and Mathematics Commons™
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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Homeomorphisms Of The Sierpinski Carpet, Karuna S. Sangam
Homeomorphisms Of The Sierpinski Carpet, Karuna S. Sangam
Senior Projects Spring 2018
The Sierpinski carpet is a fractal formed by dividing the unit square into nine congruent squares, removing the center one, and repeating the process for each of the eight remaining squares, continuing infinitely many times. It is a well-known fractal with many fascinating topological properties that appears in a variety of different contexts, including as rational Julia sets. In this project, we study self-homeomorphisms of the Sierpinski carpet. We investigate the structure of the homeomorphism group, identify its finite subgroups, and attempt to define a transducer homeomorphism of the carpet. In particular, we find that the symmetry groups of platonic …
Graph Replacement Systems For Julia Sets Of Quadratic Polynomials, Yuan Jessica Liu
Graph Replacement Systems For Julia Sets Of Quadratic Polynomials, Yuan Jessica Liu
Senior Projects Spring 2018
Belk and Forrest construct a specific class of graph replacement systems that give sequences of graphs that converge to fractals. Given a polynomial, we have an algorithm that gives a replacement system that leads to a graph sequence which we conjecture converges to the Julia set. We prove the conjecture for the quadratic polynomial $z^2+c$ where $c$ is a real number and the critical point is in a three cycle. We present some additional results and observations on replacement systems obtained from certain polynomials.
Concerning The Construction Of Four-Bar Linkages And Their Topological Configuration-Spaces, Peter K. Servatius
Concerning The Construction Of Four-Bar Linkages And Their Topological Configuration-Spaces, Peter K. Servatius
Senior Projects Spring 2018
For a given linkage with one degree of freedom we can analyze the coupler curve created by any selected tracer point in relation to a driver link. The Watt Engine is a four-bar linkage constructed such that the tracer point draws an approximate straight line along a section of the coupler curve. We will explore the family of linkages that are created using Watt's parameters, along with linkages designed by other inventors; looking at methodologies of creating a linkage and the defining what we mean by approximate straight-line motion. Ultimately we will be creating our own linkage using what we …
Hyperplanes Equipartition With Cascading Makeev, Jialin Zhang
Hyperplanes Equipartition With Cascading Makeev, Jialin Zhang
Senior Projects Spring 2018
Given a finite number of masses in the Euclidean space, one could ask is it possible to equipartition these masses into equal parts. Fixing the collection of masses, and the amount of hyperplanes, the equipartition-ability depends on the dimension, and there exists a dimension of such equipartition is possible. In this paper, topology and combinatorics method are used for estimating the lower bound and upper bound of the dimension. In particular, we are looking equipartition problem together with Cascading Makeev Constrain.