# Category Summer Semester 2022

## 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…

## Hyperbolic Game Engine

Written by Ines Bultmann and Filippa Piazolo The goal of our project was to design a 2D hyperbolic game engine in p5.js using the Poincaré disk as the hyperbolic model. The inspiration for the game engine came from the arcade…

## Visualizing the Hopf fibration

Written by Jonas Höcht, Burak Ertan und Carola Behr The famous physicist Sir Roger Penrose called the Hopf fibration “an element of the architecture of our world” – reason enough to try and visualize this remarkable map. Through the formalism…