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Earth's surface materials constitute the basis for life and natural resources. Most of these materials can be catergorized as soft matter, yet a general physical understanding of the ground beneath our feet is still lacking. Here we provide some perspectives. 

We use well resolved numerical simulations with the lattice Boltzmann method to study Rayleigh–Bénard convection in cells with a fractal boundary in two dimensions for $Pr = 1$ and $$Ra \in \left [10^7, 10^{10}\right ]$$ , where Pr and Ra are the Prandtl and Rayleigh numbers. The fractal boundaries are functions characterized by power spectral densities $S(k)$ that decay with wavenumber, $$k$$ , as $$S(k) \sim k^{p}$$ ( $p < 0$ ). The degree of roughness is quantified by the exponent $$p$$ with $p < -3$ for smooth (differentiable) surfaces and $$-3 \le p < -1$$ for rough surfaces with Hausdorff dimension $$D_f=\frac {1}{2}(p+5)$$ . By computing the exponent $$\beta$$ using power law fits of $$Nu \sim Ra^{\beta }$$ , where $Nu$ is the Nusselt number, we find that the heat transport scaling increases with roughness through the top two decades of $$Ra \in \left [10^8, 10^{10}\right ]$$ . For $$p$$ $= -3.0$ , $-2.0$ and $-1.5$ we find $$\beta = 0.288 \pm 0.005, 0.329 \pm 0.006$$ and $$0.352 \pm 0.011$$ , respectively. We also find that the Reynolds number, $Re$ , scales as $$Re \sim Ra^{\xi }$$ , where $$\xi \approx 0.57$$ over $$Ra \in \left [10^7, 10^{10}\right ]$$ , for all $$p$$ used in the study. For a given value of $$p$$ , the averaged $Nu$ and $Re$ are insensitive to the specific realization of the roughness.