To study the nonlinear physics of incompressible turbulent flow, the unaveraged Navier–Stokes equations are solved numerically. Initial three‐dimensional cosine velocity fluctuations and periodic boundary conditions are used. No mean gradients are present. The three components of the mean‐square velocity fluctuations are equal for the initial conditions chosen. The resulting solution shows characteristics of turbulence, such as the nonlinear excitation of small‐scale fluctuations. For the higher Reynolds numbers the initially nonrandom flow develops into an apparently random turbulence. Thus, randomness or turbulence can apparently arise as a consequence of the structure of the Navier–Stokes equations.