We propose two attention functions that capture cross-channel statistical scaling regularities: Monofractal and Multifractal recalibration. We build an experimental framework centered around the U-Net [1] and show that these approaches, especially Multifractal recalibration, lead to substantial improvements over a baseline augmented with other attention functions that may also describe each channel in terms of higher-order statistics [2]-[4]. Our experiments cover three public datasets from diverse modalities: ISIC18 (dermoscopy) [5], Kvasir-SEG (endoscopy) [6], and BUSI (ultrasound) [7]. Additionally, we also study the dynamics of the Squeezeand-Excite attention layer [8] and our findings suggest that (a) excitation response does not get increasingly specialized with encoder depth in the U-Net due to its skip connections, and that its effectiveness may be linked to global statistics of their instance-variability. To the best of our knowledge, we present the first instance of end-to-end multifractal analysis for semantic segmentation.