This is a
Fillomino
puzzle where every polyomino is required to be an L-shape, as in
Sashigane.
Write a number in every empty cell so that every group of cells with the
same number that is connected through its edges is an L-shape (with arms
of positive length and 1-cell thickness) with that number of cells.
May be slightly reminiscent of
no-rectangle
Fillominoes. Slightly… (Has anybody done this before? It
seems so interesting that I feel like I couldn’t be first.)
Hey, a “theme” (look at the corners)!

Honestly though I’m just spreading out my puzzle posts so there’s
some illusion of regularity.
Not actually my first try, but I guess I don’t need to resort to 6x6s
to fill up my quota just yet, do I?

Okay for the absolutely uninformed, this is a
Fillomino
(or see
MellowMelon’s rule
page).
I’ve switched to 32x32 pixel cells because they seem a reasonable
size and it’s possible to express all pixel sizes as an exact
floating-point fraction of the cell side so my image generator can be
used in a general way to get perfect stroke thicknesses without worrying
about any rounding errors no matter how obviously numerically
insignificant they would be in this case.