Judith A Palagallo

Nanoassembly of a Fractal Polymer: A Molecular Sierpinski "Hexagonal Gasket"

Mathematics and art converge in the fractal forms that also abound in nature. We used molecular self-assembly to create a synthetic, nanometer-scale, Sierpinski hexagonal gasket. This nondendritic, perfectly self-similar fractal macromolecule is composed of bis-terpyridine building blocks that are bound together by coordination to 36 Ru and 6 Fe ions to form a nearly planar array of increasingly larger hexagons around a hollow center.

FRACTAL TILINGS IN THE PLANE

Tilings have appeared in human activity since prehistoric times. They are used in the design of floor and wall coverings for cathedrals, commercial buildings, and personal dwellings. Mathematicians stucly the geometric structure of tilings. A checkerboard is an elementary example of a sinilarity tiling, one that is composed of smaller tiles (,rep tiles) of the same size, each having the same shape as the whole. Each rep tile in the checkerboard is the scaled and translated image of the entire board. For the checkerboard in FIGURE la, the lower left tile is the image of the checkerboard under