An outstanding puzzle in Quantum Gravity is the strange coincidence that two of the most developed approaches both produce a continuum (by different means) which looks normal 4D at large scale but at micro scale the dimensionality gradually declines to around 2D. That is the micro geometry becomes chaotic and like a fractal or a foam. In neither approach were they expecting this to happen. They just built a quantum version of General Relativity (in two different ways) and then in the process of exploring they both came across this surprising micro fractal-like geometry. Empirically, so to speak. In one case it came out of computer simulations of small quantum universes (Loll CDT Triangulations approach) and in another it came analytically using a putative fixed point of the renormalization group flow (Reuter ERG exact renormalization group method also called QEG quantum einstein gravity.) So we have this odd coincidence. Two very different theory approaches seem to point to the same thing. Could it actually be true about nature. And true or not, how can one explain the coincidence. In both the dimensionality unexpectedly declines smoothly to 2D at small scale. OK so Benedetti just got his PhD with Loll at Utrecht and went to postdoc at Perimeter. And he has proposed in this little 4 page paper an idea of what might be a kinship between the two non-classical continuums that might explain this coincidence. I put it out in case anyone can comment. I would like to see anyone's ideas about this. http://arxiv.org/abs/0811.1396 Fractal properties of quantum spacetime Dario Benedetti 4 pages, 2 figures (Submitted on 10 Nov 2008) "We show that in general a spacetime having a quantum group symmetry has also a scale dependent fractal dimension which deviates from its classical value at short scales, a phenomenon that resembles what observed in some approaches to quantum gravity. In particular we analyze the cases of a quantum sphere and of k-Minkowski, the latter being relevant in the context of quantum gravity."