The problem of the roll up of a two dimensional vortex sheet generated by a wing in an ideal fluid is phrased in terms of the streamfunction and the vortex sheet strength. A numerical method is used to calculate the time evolution of the vortex sheet by adapting the "Cloud In Cell" technique introduced in solving many particle simulations in plasma physics (see J.P. Christiansen, J. Computational Physics 13 (1973)). Two cases are considered for the initial distribution of circulation, one corresponding to an elliptically loaded wing and the other simulating the wing with a flap deployed. Results indicate that small scale behaviour plays an important part in the roll up. Typically, small scale perturbations result in small structures which evolve into ever increasing larger structures by vortex amalgamation. Conclusions are given from a number of tests exploring the validity of the method. Briefly, small scale perturbations are introduced artificially by the grid; but once the process of vortex amalgamation is well underway, the emerging large scale behaviour is relatively insensitive to the precise details of the initial perturbations. Since clearly defined structures result from the application of this method, it promises to aid considerably in understanding the behaviour of vortex wakes.