Interface Region Imaging Spectrograph (IRIS) Observations of the Fractal Dimension in the Solar Atmosphere

While previous work explored the fractality and self-organized criticality (SOC) of flares and nanoflares in wavelengths emitted in the solar corona (such as in hard X-rays, soft X-rays, and EUV wavelenghts), we focus here on impulsive phenomena in the photosphere and transition region, as observed with the {\sl Interface Region Imaging Spectrograph (IRIS)} in the temperature range of $T_e\approx {10}^4-{10}^6$ K. We find the following fractal dimensions (in increasing order): $D_A=1.21\pm 0.07$ for photospheric granulation, $D_A=1.29\pm 0.15$ for plages in the transition region, $D_A=1.54\pm 0.16$ for sunspots in the transition region, $D_A=1.59\pm 0.08$ for magnetograms in active regions, $D_A=1.56\pm 0.08$ for EUV nanoflares, $D_A=1.76\pm 0.14$ for large solar flares, and up to $D_A=1.89\pm 0.05$ for the largest X-class flares. We interpret low values of the fractal dimension ($1.0\text{lapprox}{D}_A\text{lapprox}1.5$) in terms of sparse curvi-linear flow patterns, while high values of the fractal dimension ($1.5\text{lapprox}{D}_A\text{lapprox}2.0$) indicate near space-filling transport processes, such as chromospheric evaporation. Phenomena in the solar transition region appear to be consistent with SOC models, based on their size distributions of fractal areas $A$ and (radiative) energies $E$, which show power law slopes of ${\alpha }_A^{obs}=2.51\pm 0.21$ (with ${\alpha }_A^{theo}=2.33$ predicted), and ${\alpha }_E^{obs}=2.03\pm 0.18$ (with ${\alpha }_E^{theo}=1.80$ predicted).