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(a)

(b)

(c)

Figure 5: An example of the algorithm, where $N_1=3,\hspace{0.17em}\hspace{0.17em}{N}_2=3,\hspace{0.17em}\hspace{0.17em}\alpha =2,$ and $n=2$. In this case, there are four regions and one domain. Thus, the RIFS is actually an IFS. The connection vector is $V=(\mathrm{1,1},\mathrm{1,1})$. The algorithm is expected to produce 81 points for the attractor. In all the figures the squares represent the projection of the points on ${ℝ}^2$. (a) The initial interpolation points are shown with black. The points of $\widehat{\mathrm{\Delta }}$ are the four corners. (b) The points produced after one iteration (c) The points produced after 2 iterations.