El Naschie’s cantorian strings and dendritic morphogenesis

One shows that the dendritic morphogenesis is induced by 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 Cantorian-fractal structure of space-time induces, by means of the dendritic growth velocities, an intrinsic anisotropy and critical wavelengths capable to cause the dendritic tip to undergo a morphological instability, and by means of the energy spectrum, forbidden energy bands. In such a space-time, the El Naschie’s Cantorian strings generate the dendritic morphogenesis.