  In the present work, the notion of Cubic Spline Super Fractal Interpolation
Function (SFIF) is introduced to simulate an object that depicts one structure
embedded into another and its approximation properties are investigated. It is
shown that, for an equidistant partition points of [x_0,x_N], the interpolating
Cubic Spline (SFIF) and their derivatives converge respectively to the data
generating function and its derivatives at the rate of h^(2-j+e) (0<e<1),
j=0,1,2 as the norm h of the partition of [x_0,x_N] approaches zero. The
convergence results for Cubic Spline (SFIF) found here show that any desired
accuracy can be achieved in the approximation of a regular data generating
function and its derivatives by a Cubic Spline (SFIF) and its corresponding
derivatives.
