Filaments and spirals in a noninteger dimensional universe

The paper presents analysis showing that the earliest structures in the evolution of noninteger dimensionality in a system will be filaments and spirals. Before the dimensionality has reached 1, the structures are linear, and thereafter these filaments or threads begin to bend and fold to be in accord with fundamental scale-invariance requirements. As the evolution proceeds, threads turn into spirals in a manner that parallels phase changes in a liquid crystal. Evidence is presented that the emergence of threads and spirals is consistent with the findings in bioscience, liquid crystals, galactic center filaments, and early spiral galaxies.