Sierpinski Triangle

fractalself-assemblysurface sciencenanotechnologymaterials sciencemolecular assemblyself-similar structuremathematical patternAu(100) surfaceultrahigh vacuumrecursive patterncetz

A Sierpiński triangle is a fractal with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles. The diagram shows a fifth-order Sierpiński triangle, which was experimentally realized out of Fe/C3PC molecules on a reconstructed Au(100)-(hex) in 10.1021/jacs.7b05720.

The visualization shows a yellow Sierpiński triangle (representing Fe/C3PC molecules) with a gold border (representing BPyB molecules) on a background of red dots arranged in a hexagonal close-packed pattern (representing the Au(100) substrate atoms). Previous molecular Sierpiński triangle fractals were limited to fourth-order due to kinetic growth constraints.