Stingray Nebula

Question

_{An entry in Fortnightly Topic Challenge #35: Restricted Title 1. Inspired by the title of this xkcd comic, but in no way related or affiliated beyond the shared name.}

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This is the stingray nebula:

Spectacular, isn't it?

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This is a nebula map of another part of the sky:

Unfortunately, it only contains data from a limited spectrum of light, so whilst you can see the stars, you can't see the nebulae themselves. I need your help restoring it...

Luckily, as with all nebula maps, it follow the standard rules, which - as I'm sure you'll recall - consist of:

1. Every square of the map belongs to exactly one nebula
2. Each nebula consists of a single set of contiguous squares connected by edges
3. All nebulae have at least one axis of reflective symmetry
4. The letter in each star is a relative magnitude indicating the number of squares in the containing nebula:
   • $A$ is strictly less than $B$, which is strictly less than $C$, and so on...
   • In this map, $A = 1$ and $L = 20$
5. Stars are considered to be part of a nebula, thus cannot be shared and must be taken into account when applying rule 3

Complete the nebula map by indicating which squares of the grid are contained within each nebula.

Answer 1

Resident Grid Detective checking in to drop off the answer to this lovely puzzle. Step by step pics coming soon.

Step by step ish:

This happens because G is at least area 7. Test the I just above G, which is now at least area 8; it doesn’t work in a nebula by itself, so it needs to join with the I above it, and with the area restriction of at least 8 you can make some progress on its shape. Now note that little cranny above the Is - This can only be accessed by the J, which tells us the axis of symmetry for the J is vertical. Also, the Es which are at least 5 get forced to join up and go down. This forces the J to expand around the A. The cell to the upper right of the J has to be taken by one of the Hs, and this only works if they join up like so. When this happens, the F gets forced down, and a lot of stuff also happened with the L - I’ll try to explain that! Essentially in the top right 4x5 area, there are 20 cells. At most 1 is taken by the F, exactly 3 by the C, at most 12 by the Ds and the rest would have to be taken by the L. This means the L has to go up into that area. L can’t have a vertical axis of symmetry (you can’t fit 20 cells like that) so a horizontal axis of symmetry forces the L to extend upwards like so. And then the Ds to the right, which we know have area 4, get forced. The cell to the lower right of the lower right A can only be taken by L, so we get more stuff. Also noticing that L can’t quite get big enough at the right side without crushing the D/Cs at the top, L has to extend left. Now the D to the upper left of L gets forced to join with the D above, and L gets forced to expand a bit more in the top left like so: Also the F in the corner got forced to join with another F by virtue of being at least 6 squares. Minor bifurcation incoming: the B above the Fs either extends left of up. If you assume it goes to the left, there’s a magic cell that needs to be taken up by K, which traps an F at the bottom like so: I forgot to mention the D extended left and up because it’s the only letter that could take those cells. Anyway that blue stuff is all bad, so the B has to actually go up instead. That forces the D to be a square. Now the blue circled area can only be taken by K or F, and it can’t all be taken by F, so K has to extend there and it can only do so in this way: This forces the E above the K down as it’s the only letter which can take that cell. This causes a chain reaction of things - the E can only be completed to 5 cells by making a T shape, Fs turn out to be size 7, and the Fs down at the bottom right almost get completed. If the currently uncompleted F takes the cells adjacent to the star, then neither K nor F can take the cell to the upper right of that F area. So the F gets completed as a sort of tilted W: and the rest is pretty easy to finish up.