I invent models to explore the physical properties of magic squares.
The water retention model progressed from the specific case of the magic square to a more generalized system of random levels. A quite interesting counter-intuitive finding that a random two-level system will retain more water than a random three-level system when the size of the square is greater than 51 X 51 was discovered. Percolation theory explains this landscape. This was reported in the Physical Review Letters in 2012 and referenced in the Nature article in 2018.
Magic Square Graphics
The illustration below is a 11 x 11 magic square depicted as a water retaining surface. The letter "H" is shown with side specific drainage to the left and to the top. Of the 26 letters, the letter H is the most difficult to make. Harry White and I wrote the American declaration of independence on the surface of a 1914 x 1914 magic square containing 8892 letters in 2014.
More recently I have tried to humanize the polyiamonds. I don't see many examples of things tiled with polyiamonds larger than the heptiamonds. Perhaps that is because the number of different polyiamonds quickly gets into the thousands. Bit map vector programming can easily take a subset of larger polyiamonds and tile a space. I give examples for various orders of polyiamonds in the following section.