Fractal Dimension of Turbulent Black Holes

We resolve a recent claim that turbulent black holes in anti-de Sitter space have event horizons with a fractal dimension greater than 3. By constructing such event horizons using turbulent fluid simulations and the fluid-gravity duality, we measure the fractal dimension of the horizon to be $\approx 2.6$. There is mounting evidence that astrophysical black holes can become turbulent, so a covariant formulation of the fractal dimension will be useful for characterizing their states.