I contacted Dr. Tiozzo about the similarity of the two fractals and he replied,
From Giulio Tiozzo
"Of course, the similarity between the set of zeros of Littlewood polynomials and Thurston’s entropy bagel is striking.
In fact, I proved a few years ago that the two fractal sets the same inside the unit disk!
The difference is that Baez’s set is symmetric under circle inversion, while Thurston’s set is not: the parts outside of the unit disk are completely different."
From Giulio Tiozzo
"Of course, the similarity between the set of zeros of Littlewood polynomials and Thurston’s entropy bagel is striking.
In fact, I proved a few years ago that the two fractal sets the same inside the unit disk!
The difference is that Baez’s set is symmetric under circle inversion, while Thurston’s set is not: the parts outside of the unit disk are completely different."