We present a novel method for the determination of the Hausdorff dimension (DH ) in coordination systems. Traditionally, DH is calculated via box-counting algorithms—a computationally intensive process sensitive to finite-size effects and noise. We demonstrate that the Hausdorff dimension is fundamentally equivalent to the ratio of energy flux (E) to information resolution (I). This arithmetic identity, G = E/I, implies that geometry itself is a projection of thermodynamic information resolution. For systems at the infrared (IR) fixed point of 3D coordination, this ratio converges to a stable universal constant (η∗ ≈ 2.52), providing a more accurate, real-time diagnostic of structural dimensionality without the need for multi-scale spatial analysis.
Lindorf Amado (Wed,) studied this question.