Resumen: Using scaling arguments and the property of self-similarity we derive the Casimir energies of Sierpinski triangles and Sierpinski rectangles. The Hausdorff-Besicovitch dimension (fractal dimension) of the Casimir energy is introduced and the Berry-Weyl conjecture is discussed for these geometries. We propose that for a class of fractals, comprising compartmentalized cavities, it is possible to establish a finite value to the Casimir energy even while the Casimir energy of the individual cavities consists of divergent terms. Idioma: Inglés DOI: 10.1103/PhysRevD.96.105010 Año: 2017 Publicado en: PHYSICAL REVIEW D 96, 10 (2017), 105010 [7 pp] ISSN: 2470-0010 Factor impacto JCR: 4.394 (2017) Categ. JCR: ASTRONOMY & ASTROPHYSICS rank: 15 / 66 = 0.227 (2017) - Q1 - T1 Categ. JCR: PHYSICS, PARTICLES & FIELDS rank: 7 / 29 = 0.241 (2017) - Q1 - T1 Factor impacto SCIMAGO: 1.801 - Physics and Astronomy (miscellaneous) (Q1)