Fractal Structure of Isothermal Lines and Loops on the Cosmic Microwave
  Background
  The statistics of isothermal lines and loops of the Cosmic Microwave
Background (CMB) radiation on the sky map is studied and the fractal structure
is confirmed in the radiation temperature fluctuation. We estimate the fractal
exponents, such as the fractal dimension $D_{\mathrm{e}}$ of the entire pattern
of isothermal lines, the fractal dimension $D_{\mathrm{c}}$ of a single
isothermal line, the exponent $\zeta$ in Kor\v{c}ak's law for the size
distribution of isothermal loops, the two kind of Hurst exponents,
$H_{\mathrm{e}}$ for the profile of the CMB radiation temperature, and
$H_{\mathrm{c}}$ for a single isothermal line. We also perform fractal analysis
of two artificial sky maps simulated by a standard model in physical cosmology,
the WMAP best-fit $\Lambda$ Cold Dark Matter ($\Lambda$CDM) model, and by the
Gaussian free model of rough surfaces. The temperature fluctuations of the real
CMB radiation and in the simulation using the $\Lambda$CDM model are
non-Gaussian, in the sense that the displacement of isothermal lines and loops
has an antipersistent property indicated by $H_{\mathrm{e}} \simeq 0.23 < 1/2$.
