Abstract
One shows that the dendritic morphogenesis is induced by one-dimensional cnoidal thermal oscillation modes of the solid-liquid interface. Particularly, the one-dimensional l-thermal antisoliton — one-dimensional l-thermal soliton modes imposes laws characterizing dendritic branches growth. One deduces a relation between the dendritic growth speed and the dendritic tip radius that depends on the supercooling degree. Particularly one obtains the Oldsfield's relation. The variation of the fractal dimension with the supercooling degree specifies that the dendritic growth are two-dimensional projections of a higher-dimensional fractal.
