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(a)

(b)

(c)

(d)

(e)

Figure 4: An example of the construction. Here $N_1=N_2=5$, the regions have dimensions $0.25\times 0.25$ and the domains $0.5\times 0.5$. We used Laplace's partial differential equation (${\partial }^{2}g/\partial x^2+{\partial }^{2}g/\partial y^2=0$) with Dirichlet's boundary conditions. (a) The set of interpolation points. (b) The function $h$. (c) The function $H$. (d) The function $B$. (e) The fractal interpolation surface.