  We estimate the bounds of box-counting dimension of hidden variable fractal
interpolation functions (HVFIFs) and hidden variable bivariate fractal
interpolation functions (HVBFIFs) with four function contractivity factors and
present analytic properties of HVFIFs which are constructed to ensure more
flexibility and diversity in modeling natural phenomena. Firstly, we construct
the HVFIFs and analyze their smoothness and stability. Secondly, we obtain the
lower and upper bounds of box-counting dimension of the HVFIFs. Finally, in the
similar way, we get the lower and upper bounds of box-counting dimension of
HVBFIFs constructed in [21].
