I have been recently involved in creating "mathematical" objects and pictures. Somme of the objects here were made by Elena Willis during an internship under my supervision.
All the pictures and videos are under the license Creative Commons (CC BY-NC-ND 3.0)
A pantograph is a device to "realize" homothety. While the user is drawing with one pen the other pen is reproducing the same picture under an homothety (here with ratio 2). The Sylvester machine works in the same way and "realizes" a positive similarity.
Some Julia sets associated to the complex transformation $z \to z^2 + c$.
Two quasi-periodic Penrose tillings