Interface region imaging spectrograph (IRIS) observations of the fractal dimension in the solar atmosphere

We focus here on impulsive phenomena and Quiet-Sun features in the solar transition region, observed with the Interface Region Imaging Spectrograph (IRIS) at 1,400 angstrom (at formation temperatures of T-e approximate to 10(4)-10(6) K). Summarizing additional literature values we find the following fractal dimensions (in increasing order): D-A = 1.23 +/- 0.09 for photospheric granulation, D-A =1.40 +/- 0.09 for chromospheric (network) patterns, D-A = 1.54 +/- 0.04 for plages in the transition region, D-A = 1.56 +/- 0.08 for extreme ultra-violet (EUV) nanoflares, D-A = 1.59 +/- 0.20 for active regions in photospheric magnetograms, and D-A = 1.76 +/- 0.14 for large solar flares. We interpret low values of the fractal dimension (1.0 less than or similar to D-A less than or similar to 1.5) in terms of sparse curvi-linear flow patterns, while high values of the fractal dimension (1.5 less than or similar to D-A less than or similar to 2.0) indicate quasi-space-filling transport processes, such as chromospheric evaporation in flares. Phenomena in the solar transition region appear to be consistent with self-organized criticality (SOC) models, based on their fractality and their size distributions of fractal areas A and (radiative) energies E, which show power law slopes of alpha(obs)(A)=2.51 +/- 0.21 (with alpha(theo)(A)=2.33 predicted), and alpha(obs)(E)=2.03 +/- 0.18 (with alpha(theo)(E)=1.80 predicted). This agreement suggests that brightenings detected with IRIS at 1,400 angstrom reveal the same nonlinear SOC statistics as their coronal counterparts in EUV.