national audience The urban economy in Thünen is a remarkable abstraction: its family of models retains key features of the infinite complexity of real cities. However, it is less suited to modern urban forms (polycentrism, relaxation of centripelet forces, etc.), especially to the peri-urban area, as it is a mixed space. This leads the authors to propose a model that keeps a classic microeconomic programme in urban economics, but works in the geometry of a Sierpinski carpet, a fractal that allows a hierarchical link between rural areas and urban centres in a metropolitan area to be stylised. A household maximises, under budgetary constraints, a utility function Cobb-Douglas-ETUC, with ETUC sub-functions reflecting the taste for the variety of urban and rural amenities. The balance is achieved on the land market, based on the microeconomic optimum of households. The latter depends on the accessibility of the various facilities according to their hierarchical rank, that is to say, finally, the distances which are calculated according to the Sierpinski carpet metric. The distances between the grid cells for this fractal are calculated. The model accepts an analytical solution supplemented by numerical simulations that show the effects of fractional geometry. The land yield gradient depends on accessibility to urban and rural amenities and it is no longer, as in Thünen, a monotone in the original distance. The fractional shape produces significantly different results from the Thünian city when the cost of alternating migration is low, the taste for their development is important or the substitutability of these arrangements between them is low.