Is there a way that I could make a randomly generated map (random enough to look like the ones in the images), while still using a TileD format?

I'm thinking maybe the Tiled map, could just be a big rectangle while the tiles inside don't permit entry to outer zones, but this needs to be generated via function somehow. Ideas would be appreciated!

(where the dark red is the boundries)
I was thinking of something like this, the boundries are calculated based on wether the point is closer to (x,y) or (x - 1, y) etc

I would really prefer a Tiled map though, although if it's in no way possible, I can use an Array[][]. (If it's not possible with Tiled, and I have to use an array can I still get the help for it please?)
Edit: So I just made this, and I'll be able to use a point in the middle of each tile to see if it is eligible to be a piece of ground. The math/shapes will change the make it broader with less nooks/crannies etc.
Edit2: So now I've got this; The circles have to be touching, or they get remade (onto the last circle that made it)

Now I'm about to write a function (I've got it in psuedocode) to turn these shapes into tile objects.
I have pretty much answered my own question, but I've not finished yet!