Computational modelling techniques have been applied in physics, biology and other fields for decades to investigate the scale-invariant properties in non-equilibrium complex (many-cell) systems. Specific examples have been considered to underpin the simulation of cellular systems, le sandpiles as simple models of transport phenomena, and soap froths as models of many-cell cellular networks. A number of characteristic properties have been investigated to explore common features of complex systems. Particularly interesting for the simple sandpile automaton is the achievement of the critical state through the phenomenon known as self-organised criticality (SOC). Various simulation algorithms eg cellular automata, direct simulation and Monte Carlo have been used to model the sandpile and froth systems respectively. The studies of a directed and dissipative CML sandpile model provide evidence for the occurrence of SOC, with the system characterised by simple power-law distributions. For the soap froth model, the effect on the evolution of the presence of defects is investigated, together with the impressions of varying the amount of disorder Scaling properties obtained, for various initial conditions, are given in detail. The improvements on methods of computational modelling, and the limitations of software and hardware implementation are also briefly discussed.