Magic Square - Physical Properties
The image below shows areas surrounded by larger numbers with a blue background. A water retention topographical model is one example of 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. This was reported in the Physical Review Letters in 2012 and referenced in the Nature article in 2018.
Magic Square Material
Associative Magic Square
Humanizing the Polyiamonds
The graphic below is composed of objects made from polyiamonds that contain 15 triangles. There seems to have been little attempt to tile things with polyiamonds larger than heptiamonds. Perhaps this is because the number of different polyiamonds quickly gets into the thousands. Bit map vector programming can easily take a limited set of larger tiles and tile a space. The link below gives examples for the polyiamonds from 5 to 21 unit triangles.
|Wikimedia Commons has media related to Knecht03/sandbox.|