What is known about the area of the symmetric Pythagorean tree? (Closed unit square as base, area of enclosed triangles not included.) The problem in calculating the area is that squares start to overlap from the sixth iteration onwards.

Without much effort it can be computed that height is 4 and breadth is 6, so an upper bound for the area is 24. Wikipedia reports that lower and upper bounds can with some effort be tightened to 5 and 18, respectively. The accompanying Wikipedia talk page reports on numerical approximations (pixel counts) that end somewhere near 14. Other than that, no trace of a hint of an exact answer in the literature.

Seems like a simple high-school problem. On closer inspection I believe it is not, due to the problem of overlapping squares.

pro temexplanation is good enough for me. It would be ridiculous to hold every MO question to the same standard (explain to me why I should care), and in my view many other questions that appear on MO are of even less intrinsic interest. I expect the problem is indeed challenging. People should work on it only if they feel like it. – Todd Trimble♦ May 9 '13 at 16:57