Figure 3.

Main curve, the configuration entropy $S/k_B$ of proto-tissues as a function of the spatial dimension $d$. The maximum occurs numerically at $d~2.5$ and promotes diversity and complexity. Inset curve, the derivative $\gamma =\left(1/k_B\right)\partial S/\partial d$ defines equilibrium in a system with uncertain (fluctuating) spatial dimension of average $d$. At $d~5,\gamma ~0$ is related to weak thermal fluctuations ($\gamma ~\delta T/2T$) and is optimal for proto-tissue formation. The black point corresponds to $\gamma \approx 0.076$ for the Atacama Desert (Chile).