In this work we focus on steady state solutions of reaction diffusion systems with applications to biological patterns. Our goal is to investigate how domain size affects the patterns generated by the systems. We adopt Turing's idea and carry out linear stability analysis to derive the necessary conditions for diffusion driven instability. This provides for the formulation that relates the domain size to permissible wave numbers for the linearised system. To evaluate the prediction offered by the linearised system, we use an arc-length continuation method with domain size as a parameter to locate the bifurcation points. The method is implemented using a spectral collocation scheme for which orthogonal polynomials are used as base functions. Results are compared with those from the linearised system for both one and two dimensional cases.