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Construction of Sierpiński Triangles up to the Fifth Order
- Li, Chao, Zhang, Xue, Li, Na, Wang, Yawei, Yang, Jiajia, Gu, Gaochen, Zhang, Yajie, Hou, Shimin, Peng, Lianmao, Wu, Kai, Nieckarz, Damian, Szabelski, Paweł, Tang, Hao, Wang, Yongfeng
- Journal of the American Chemical Society 2017 v.139 no.39 pp. 13749-13753
- aesthetics, benzene, gold, iron, mathematics
- Self-similar fractal structures are of fundamental importance in science, mathematics, and aesthetics. A series of molecular defect-free Sierpiński triangle fractals have been constructed on surfaces recently. However, the highest order of the fractals is only 4 because of the limitation of kinetic growth. Here complete fifth-order Sierpiński triangles with a lateral length of 0.05 μm were successfully prepared in ultrahigh vacuum by a combination of templating and coassembly methods. Fe atoms, 4,4″-dicyano-1,1′:3′,1″-terphenyl, and 1,3-bis(4-pyridyl)benzene molecules were used to build fractals on the reconstructed Au(100)-(hex) surface. The new strategy may be applied to construct various Sierpiński triangles of higher orders.