Splitting fingers under strain: Pattern formation of a dipolar fluid in a polymer medium

We study the formation and evolution of labyrinthine patterns for dipolar f luids inside a polymer medium under mechanical strain. A new general mechan ism is proposed to describe the kinetics of the pattern formation that comb ines orientation ordering and subsequently breaking characteristics of dipo lar fluids with branching characteristics of crack-propagation This mechani sm can lead to many of the patterns found in nature, including spots, strip es, labyrinthine, and starlike formations.