Cross-Domain Transfer of a Fractal Box-Counting Complexity Diagnostic: From Divertor Heat-Flux Profiles to Human EEG States

AbstractThe Improved Gradient Fractal Dimension diagnostic (IGFD) was originally developed to quantifythe box-counting fractal dimension of divertor heat-flux profiles in magnetically confined fusionplasmas. This note reports a deliberately out-of-domain validation exercise: the same box-countingpipeline, adapted with a noise-floor–calibrated scale range and Takens delay embedding, is appliedto human scalp and intracranial electroencephalogram (EEG) recordings from the publicly avail-able Bonn EEG database [1]. Across three physiological states – healthy resting wakefulness (SetB), interictal epileptic activity (Set C), and active seizure (Set E), N = 100 recordings per class –IGFD recovers a statistically significant, monotonically decreasing fractal dimension from health toseizure (D = 2.350 ± 0.108, 2.130 ± 0.144, 2.014 ± 0.300 respectively; Kruskal-Wallis H = 112.9,p = 3.0×10−25 ; all three pairwise contrasts significant at N = 100). This result is qualitatively con-sistent with, and does not supersede, decades of established findings that seizure activity correspondsto reduced dynamical complexity through neural hypersynchronization. We report this as a cross-domain methodological replication – evidence that a diagnostic tool built for an unrelated physicalsystem generalizes to biological time series once a methodological pitfall (uncontrolled noise-floorbias at fine box scales) is identified and corrected – and not as a novel neuroscientific finding. Fullmethodological limitations, including a documented erratum from an intermediate calibration test,are reported explicitly.Keywords: fractal dimension, box-counting, EEG, epilepsy, complexity, cross-domain validation, delayembedding