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 ($1.0 \lapprox D_A \lapprox 1.5$) in terms of sparse curvi-linear flow patterns, while high values of the fractal dimension ($1.5 \lapprox D_A \lapprox 2.0$) 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).