Continuous Cellular Automata
In a Cellular Automata, we simulate a grid of cells. For each cell, we can calculate its upcoming state based on its previous state. A very famous example of such a system is Conway’s Game of Life. In the Game…
Political Geometry
A comprehensive study on cooperation and cosponsoring in the US Senate Written by Ayşegül Peközsoy, Leo Späth, and Klaus Stier Political Background The United States of America is a federal republic with a presidential system, meaning that the executive branch…
Physical Graph Layout in Hyperbolic Space
Written by David Li, Anna Roth Introduction Visual graph layouts are a nice tool to quickly spot symmetries and other structures on graphs. As common graph layout tools, such as Gephi, can only layout graphs in Euclidean space, our goal…
Root Systems and their Weyl Groups
Written by Amelie Strupp Introduction This project aimed at providing an interactive application to visualize Root Systems and theircorresponding Weyl groups. The final version is available through the following link. Prerequisites This section introduces some important concepts by using visualizations…
Pascal’s theorem and Poncelets Porism
Written by Lukas Schmidt, Miriam Compton and Lena Becker Introduction During this past winter semester, we dealt with two different geometric statements: Pascal’s theorem and Poncelet’s Porism. Pascal’s theorem Let us consider six points such that if for all which…
Quasicrystals
Written by Noah Koopmann and Ingmar Lowack Due to the nature of our project, respectively the amount of subject-related text on our web application (see here), we will use the space of this blog post to talk about our work…
Rolling Knots
Written by Leon-Josip Dzojic, Matilde Sciortino, and Pirmin Kupffer In the year 1980 M. H. Freedman conjectured that every generic smooth knot in three dimensional Euclidean space has a tritangent plane, i.e., a plane tangent to three distinct points. However,…
Visualizing Topology and Geometry with a Physics Connection
Written by Ricardo Waibel in collaboration with Donald Youmans Topology and geometry are important concepts in mathematics and physics. Especially in theories like general relativity they have a direct impact, as the spacetime description of a system is already quite…
Indra’s Pearls
Written by Alassane Diagne and Ayşegül Peközsoy Möbius transformations are functions of the form \(T\colon \mathbb{C}\rightarrow\mathbb{C},\ T(z) = \frac{az+b}{cz+d}\) with \(a\), \(b\), \(c\), \(d\) complex numbers. We often associate the mapping \(T\) with the matrix \(T=\begin{pmatrix}a&b\\ c&d\end{pmatrix}\). If you look…
Mobius Paint
Written by Mouna Deubler, Yunus Sahin and Juliane Stehle During the summer term 2022, our group worked on a painting app in Hyperbolic Space of dimension two.Our goal was to create an editor for drawing, but not in the Euclidean…