Gibson scaling and related properties of flame-surface geometry in turbulent premixed combustion are demonstrated using a novel computational model, Deterministic Turbulent Mixing (DTM). In DTM turbulent advection is represented by a sequence of maps applied to the computational domain. The structure of the mapping sequence incorporates pertinent scaling properties of the turbulent cascade, Here, combustion in Kolmogorov turbulence (kinetic-energy cascade) and in Bolgiano-Obukhov convective turbulence (potential-energy cascade) is simulated. Implications with regard to chemical flames and astrophysical (thermonuclear) flames are noted.