Regarding the concept of a subquantum scale that has a strongly self-similar (fractal) correspondence to atomic scale phenomena, here is one of Discrete Scale Relativity’s definitive predictions. It is from a set of 15 such predictions.
“9. Subquantum Scale systems with radii on the order of 10^–31 cm [individual particles], 10^–30 cm to 10^–29 cm [high energy clusters of particles], and 10^–26 cm [Subquantum Scale atom analogues] should eventually be observed in ultra-fine-scale fluctuation experiments. These predicted values are 100 to 10,000,000 times larger than the putative conventional Planck length. Observational hints of such Subquantum Scale gravitational signatures in the 10^–31 cm to 10^–26 cm range have been seen in experiments at HERA (2.57 +/- 0.71 x 10^–26 cm) and at SLC (3.50 +/- 0.04 x 10^–28 cm), as reported by V. Gharibyan, Physical Review Lett., 109, 141103, 2012 [ http://arxiv.org/abs/1207.7297 ].”
For much more on a fractal cosmological paradigm, see: