Cardiac fibrillation a ects the atria or the ventricles and, in both cases, poses major challenges to public health management. Atrial fibrillation is the predominant cause of embolic stroke while ventricular fibrillation leads to sudden cardiac arrest and death. The medical community of cardiac electro-physiologists consider cardiac fibrillation as a disease of known cause, namely a chaotic multiplication of electric pulse reentries, but of unknown trigger. Putative triggers are targeted in an e ort to solve this riddle by a combination of safe therapies including anti-arrhythmic drugs and catheter radio-frequency ablation. In two recent works (10.3389/fphys.2017.01139 and 10.3389/fphys.2019.00480), with Evgeniya Gerasimova Françoise Argoul and Alain Arneodo, we have provided evidence and modeling which clash with the accepted wisdom. We give here the main argument for the incompatibility of the random multifractal scaling, revealed in recordings of the electrical activity of fibrillating human hearts, with the reentry paradigm. In the model, pulse dynamics is akin to a random branching birth and death process due to a highly fluctuating conductance. In this respect, we sketch a calculation of the multifractal spectrum for our cardiac modeling, which underlines how the multifractal parameter is related to the variance of the abnormal capacitive electric field at the gap junction channels. Those new observations and modeling raise a number of theoretical and practical possibilities and new challenges, such as electric recording interpretation from the level of cell-to-cell coupling up to the level of neural modulations. Gray area Is atrial fibrillation characterized only by spatio-temporal irregularity of local beat-to-beat cycles? Figure 1: Left: Atrial fibrillation schematic mechanisms. Right: High density mapping of activation times.