Sometimes I doodle fib spirals on graph paper during math class. You draw a quarter circle through squares equal to the element in the series.
Like, 1 and 1 through single squares making a semi-circle. 2 is a quarter-circle through 2x2 squares and so on.
It strikes me that you could partition the rooms after this model but you would end just end up with a bunch of squares that don't seem super interesting.
Maybe make multiple fib spirals and see if the squares or spiral lines intersect in some pleasing way and base the dungeon on whatever you find.
Could be cool if the dungeon was organic and the first squares in each spiral represents a spore from which the rooms sprout.