Here is some background on Leonardo Modesto's new paper: It is in this context that Leonardo Modesto has shown that LQG also has this curious fractal-like microstructure down near Planck scale. That the dimensionality declines from the usual 4D at large scale down to 2D at the microscopic level. The measure of dimensionality he used was the diffusion or random-walk-based spectral dimension. One tells the dimensionality of the space one is in by seeing how easily a random walker gets lost in it. Dimensionality measured this way can take on fractional values. It is interesting that all three approaches (Loll Blocks, Reuter Asymptotic, and LQG) came to this same conclusion about the chaotic fractally microstructure---all three seem to present a new idea of the continuum which is smooth at large and rough at small distances. But they come at this conclusion by very different analytical methods. In any case, whether this new model of the continuum is correct or not, here is Modesto's December 2008 paper. It is only 5 pages!: http://arxiv.org/abs/0812.2214 Fractal Structure of Loop Quantum Gravity Leonardo Modesto 5 pages, 5 figures (Submitted on 11 Dec 2008) "In this paper we have calculated the spectral dimension of loop quantum gravity (LQG) using simple arguments coming from the area spectrum at different length scales. We have obtained that the spectral dimension of the spatial section runs from 2 to 3, across a 1.5 phase, when the energy of a probe scalar field decreases from high to low energy. We have calculated the spectral dimension of the space-time also using results from spin-foam models, obtaining a 2-dimensional effective manifold at high energy. Our result is consistent with two other approaches to non-perturbative quantum gravity: causal dynamical triangulation and asymptotic safety quantum gravity."