Submitted by Alexander Kröller on
The Art Gallery problem is a classic problem in Computational Geometry: Given an art gallery (a polygon), how many stationary guards do you need to guard it? We show practical applications of this problem and how it can be solved.
Submitted by Alexander Kröller on
In this video we show how to enumerate polyominoes on twisted cylinders, and explain how to use them for setting lower bounds on the asymptotic growth rate of polyominoes in the plane.
Submitted by Torolf Sauermann on
K3DSurf is a program to visualize and manipulate Mathematical models in three, four, five and six dimensions. K3DSurf supports Parametric equations and Isosurfaces.
Submitted by Jeremie Brunet on
3D fractal trip made with Mandelbulb3D
Submitted by Jeremie Brunet on
3D fractal trip made with Mandelbulb3D
Submitted by Jeremie Brunet on
3D fractal trip made with Mandelbulb3D
Submitted by Alexander Kröller on
How can a robot swarm explore an unknown area and understand its layout? In this video, a swarm of R-one mobile robots is used for such a task. They are not trying to build an accurate floor plan, which requires expensive sensors. Instead, they sketch the area using a mathematical structure - a triangulation, which captures the essential topological features of the environment. This structure can be used to help other robots navigate through the area, and it can be created by low-cost robots with limited capabilities.
Submitted by Stepan Tersian on
I made a Gallery 2, named “Estrellas de Galicia y Lisboa”. It became after Gallery 1, inspired by the exhibition of Imaginary at Santiago de Compostela, Spain. I was motivated by several images with mathematical content and stars which I met during my visit in Santiago de Compostela and Lisbon. They are completed by plots of stellated and truncated polyhedrons and stars made by Mathematica.
Submitted by Xavier De Clippeleir on
Slinky, the metal spring toy that walks down stairs has been my key inspiration. When squeezed it forms a cylinder with an ellips as cross section. The endings remain circular, parallel or anti-parallel. The parts are assembled to make flexible structures. They led to the discovery of several transforming polyhedra.
Submitted by Anna Ursyn on
I drew inspiration for my Visible Geometry series from drawing exercises I owe to studying geometry. Typically; my creation process runs through several stages. First I draw abstract geometric designs for executing my computer programs. I use the computer on different levels. Some of my computer programs produce two-dimensional images; others are three — depending on my composition’s final dictates. Then I add photographic content using scanners and digital cameras. The programs that produce two-dimensional artwork serve as a point of departure for prints on canvas and paper.