“Seahorses” in Mathematical, Physical and Biological Systems

We describe the formation of unique “seahorse” fractal patterns in the growth of fullerene-tetracyanoquinodimethane (C60-TCNQ) and pure TCNQ thin films. These “seahorse”patterns are S-shaped forms with “fins” on the outer edges of the curved arms, like real biological seahorses. These “seahorse” fractal patterns exhibit an approximate symmetry under rotation by 180°, but strongly break two-dimensional inversion symmetry. Similar “seahorse” patterns can also be simulated by the Julia set from a pure mathematical mapping of the function in complex space: z→z2+c, with c=-0.74543+0.1130i. A novel formation mechanism is proposed, involving the charging of part of the neutral molecules and clusters in the initial stage of film growth, and the broken symmetry arising from the Coulomb repulsive force in the nucleation and aggregation process. The similarity of physical, biological and mathematical seahorses shows the consistency of nature, which should stimulate our interest for deeper scientific explorations.