When a system with continuous symmetry is quenched instantly to a broken symmetry state, new phases oftopological defects appear in an otherwise homogeneous medium of continuous symmetry. The phenomenon of newphase formation is a representative example of first order transition. The phenomenon is of immense interest as anexample of a highly nonlinear process far from equilibrium. The second phase grows with time and in late stages alldomain sizes are much larger than all microscopic lengths. In the large time limit, the new phase forming systemsexhibit self-similar growth pattern with dilation symmetry, with time dependent scale, and scaling phenomenon.Extensive investigations on dynamical scaling phenomenon have been carried out so far for Euclidean systems. Thequestion arises about the validity of the scaling laws for dynamical systems in non-Euclidean fractal geometry. Some ofthe questions, arising purely because of the geometrical constraints in the physical systems and others on experimentalobservations, are posed here.Keywords: Dynamical scaling, fractals, small-angle scatteringPACS: 64.75.+g, 64.90.+b, 61.43.Hv, 61.50.Ks. S. MazumderSolid State Physics DivisionBhabha Atomic Research Centre, Trombay, Mumbai 4000 85, India