Construction of Sierpinski Triangles up to the Fifth Order

Self-similar fractal structures are of fundamental importance in science, mathematics, and aesthetics. A series of molecular defect-free Sierpifiski 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 Sierpifiski triangles with a lateral length of 0.05 itm 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 Sierpifiski triangles of higher orders.