Superconductivity associated with fractal structure of nanoscale electron lines: Said Dahmen, “We decided to make histograms of the sizes of these regions and compare them with predictions from various models. We found they agreed with those from models that also had fingery regions in the bulk of the material—the agreement was striking.”
Carlson explained, “We noticed that the pattern of orientations of the nanoscale lines doesn’t depend on the scale of the image. The pattern looks the same whether we view the entire image, or whether we view smaller and smaller pieces of it—the pattern is fractal.
“Every fractal has its own set of characteristic numbers, as unique as a fingerprint. You might imagine that the characteristic numbers for a fractal which is happening only on the surface would be different from the characteristic numbers for a fractal which really originates from deep inside the material.
“When we studied the characteristic numbers of this fractal, we discovered telltale signs in its fingerprint that indicate this is not just a surface fractal. Rather, it is coming from deep inside the material. We are seeing a 3-D fractal, which then intersects the surface of the material.”