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good day /sci/

It turns out that Penroses seminal contribution, the quasiperiodic 5-fold rotationally symmetric "penrose tiling", not discovered until the late 20th century, was employed extensively in mideval islamic architecture

https://www.youtube.com/watch?v=rldnu9rNpH8&ab_channel=PeterLu

Inevitably, this lead me to taking ancient maths, especially any fragments that may have been briefly comprehended at the height of the islamic golden age much more seriously. My question in this thread has to do with deducing a hypothesis and methodology for conducting the experiment.

Take pic related as follows, to myself imagries of a 3d cymatic took hold. Could there be a frequency, or perhaps an ensemble of frequencies that could 'carress' the geometry of the fassad.

would any anons working in the space of sonics, cymatic and the like suggest any math models that could help me find this collection of frequencies that, when played, would match the shape of the entrance?

Thanks