Centroidal Voronoi tessellations (CVTs) are Voronoi tessellations of a region such that the generating points of the tessellations are also the centroids of the corresponding Voronoi regions with respect to a given probability measure. CVT is a fundamental notion that has a wide spectrum of applications in computational science and engineering. In this paper, an algorithm is given to obtain the CVTs with n-generators to level m, for any positive integers m and n, of any Cantor set generated by a pair of self-similar mappings given by S1(x)=r1x and S2(x)=r2x+(1−r2) for x∈R, where r1,r2>0 and r1+r20 and p1+p2=1.
Dettmann, C. P., and M. K. Roychowdhury. 2021. “An Algorithm to Compute CVTs for Finitely Generated Cantor Distributions.” Southeast Asian Bulletin of Mathematics 45 (3): 173–88.
Southeast Asian Bulletin of Mathematics