I am glad to present my new Alhambra String Art in Bridges Seoul 2014. It will be exhibit in the Gwacheon National Science Museum Seoul, Korea, from August 14th to 19th, 2014. It will be also offered at the IMU DONAUCTION, in August 20th, at the ICM exhibition space. This is a public raffle organized by the International Mathematical Union, for supporting young mathematicians around the world.
This hand work reproduces the knotting structure of a famous tile in the Alhambra of Granada, Spain, also painted by M.C. Escher in 1922. We had already made this and other islamic patterns with threads and pins nailed on a wooden board, but the use of cotton thread and leather would surely be a beautiful way to represent these islamic geometric patterns at the time.
The symmetry group of this tiling is the wallpaper group P4, generated by two rotation centres of order four (90°), and one rotation centre of order two (180°). If one does not take into account the crossings, then its symmetry group is the wallpaper group PM4, generated by three mirror reflections having angles of 90º, 45º and 45º.
In the next picture you can see the fundamental domain (in yelow) of the wallpaper group P4, where the red and green squares indicate the points of order 4, and the purple rombus indicates centers of order 2:
More pictures and instructions of how to embroid this beautiful piece are available in our new web in FACEBOOK.
And also some nice views of the work, playing with the sun behind a windows, and the focus of the camera:
Virtual and manipulative geometrical and topological games 