Geometrical mosaic from the Alhambra

1 October 2025

For the #Mathober 2025 day 1 prompt ‘Link’, I offer the following image. It is based on a geometrical mosaic of intertwining loops from the Hall of the Two Sisters in the Alhambra, but has been redrawn to be mathematically exact.

An image comprising numerous interlinked loops of several colours, based on a mosaic in the Alhambra. Each loop comprises segments that are either horizontal, vertical, or diagonal at a 45 degree angle. Many loops have reflectional or rotational symmetry, and many of the loops are translationally symmetric to one another.

Here are some relevant resources:

The L^aT_eX/TikZ source code (Licensed under the L^aT_eX Project Public Licence v1.3c).
The image in PDF format. (Licensed under the Creative Commons Attribution–ShareAlike 4.0 International Licence)
Another PDF showing ‘grid coordinates’ for the mosaic. (Licensed under the Creative Commons Attribution–ShareAlike 4.0 International Licence)
A photograph of the original mosaic on Wikimedia Commons.
An illustration of the mosaic from J. Goury, O. Jones & P. de Gayangos, Plans, Elevations, Sections, and Details of the Alhambra. (London: Owen Jones, 1842–5). The book is available on the Internet Archive: volume 1, volume 2.

Although it is not required by the licences, if you use this work, a link to my book Form & Number: A History of Mathematical Beauty (for which this image was originally drawn) would be appreciated: https://archive.org/details/cain_formandnumber_ebook_large