A new geometrical framework describes the phenomenon of scale–and time–dependent dimensions observed in a great variety of multiscale systems and particularly in the field of turbulence. Based on the notions of scale entropy and scale diffusivity, it leads to a diffusion equation quantifying scale entropy and thus fractal dimension in scale space and in time. For a stationary case and a uniform sink of scale entropy flux, the fractal dimension depends linearly on the scale logarithm. Here, this is experimentally verified in the case of turbulent–flames geometry. Consequences for temporal evolution of scalar passive–turbulent interfaces are investigated and compared with experimental data. Finally, some aspects of dynamics exchange between spatial scales in a turbulent jet are also studied.