  We create a photoionization model embedded in the turbulent ISM by using the
state-of-the-art Messenger Monte-Carlo MAPPINGS~V code (M$^3$) in conjunction
with the CMFGEN stellar atmosphere model. We show that the turbulent ISM causes
the inhomogeneity of electron temperature and density within the nebula. The
fluctuation in the turbulent ISM creates complex ionization structures seen in
nearby nebulae. The inhomogeneous density distribution within the nebula
creates a significant scatter on the spatially-resolved standard optical
diagnostic diagrams, which cannot be represented by the spherical constant
density photoionization model. We analyze the dependence of different optical
emission lines on the complexity of nebular geometry, finding that the
emission-lines residing on the nebular boundary are highly sensitive to the
complexity of nebular geometry, while the emission-lines produced throughout
the nebula are sensitive to the density distribution of the ISM within the
nebula. Our fractal photoionization model demonstrates that a complex nebular
geometry is required for accurate modeling of HII regions and emission-line
galaxies, especially for the high-redshift galaxies, where the ISM is highly
turbulent based on the increasing observational evidence.

Astrophysics of Galaxies