Formula Challenge: The most efficient way to generate a Number Spiral (Ulam spiral) ?

Interesting challenge. Your frame-based REDUCE approach is clever, especially the way you isolate the 3x3 core and then expand outward by odd layers.

If the main objective is maximum size without recursion, another interesting direction would be a direct MAKEARRAY solution where each cell computes its value from its ring, side, and offset relative to the center. That would avoid repeated padding and stacking work, so it may scale better for larger spirals because each value is derived once instead of rebuilding intermediate arrays.

Either way, this is a strong example of how far LET, LAMBDA, and REDUCE can be pushed in Excel. It would be interesting to compare the runtime and max practical size of your approach versus a coordinate-based version.