The contemporary socio-spatial process on metropolises of peripheral countries reveals a number of issues that have a new level of production of space and reproduction of the social relations in accordance with the imperatives of capital accumulation. Among these issues I would like to highlight the production of the metropolitan peripheries as a key understanding to understand the process of urbanization. This position derives from the hypothesis from which the reproduction of capital, in ever broader scale, the periphery appears as renewed possibility of carrying out the reproduction of capital and now assumes new forms of metropolitan organization derived from new socio-spatial processes. In the cities there is a socio-spatial structure that organizes the distribution of population on territory and which has been updated by a new geopolitical economy of the metropolis. Thus, the argument I want to make is that, despite the new urban forms (fragmented, dispersed, extensive, diffuse, reticular) the center-periphery concept remains essential in explaining the contemporary urban phenomenon in Brazil, despite some literature point to an overcoming of this dichotomy. Therefore, it is necessary to understand this new form from a look from the redefinition of center-periphery notions of recovering these significant. The methodology is based on the definition of poverty used from the information concerning the Income Household per capita from Brazilian Census of 2000 and 2010. The article demonstrates that the spatial expansion of the analyzed cities began to acquire, especially from the twenty-first century, a new spatial expression, which I tried to call fractal periphery, that become organized spatially dispersed and fragmented way over the territory.