Six experimental investigations of pattern-formation problems are reviewed. They were chosen so as to illustrate in succession increasingly complex issues involving systems with spatial variation. The first three deal with the influence of noise, or stochastic forces, on non-equilibrium systems. A second set of experiments addresses progressively more complicated deterministic nonlinear issues. The first experiment which is discussed involves the response of a system below its first bifurcation point to external noise. The particular example studied experimentally was electro-convection in a nematic liquid crystal. The noise-induced fluctuations can be understood in terms of a linear theory. The second experiment addresses the question of how stochastic effects manifest themselves in the pattern evolution which will take place when the control parameter of the system is increased above its threshold value. This was investigated for the case of Rayleigh-Benard convection (RBC). It involves a combination of linear and weakly non-linear phenomena. The third topic deals with stochastic effects on a stationary time-periodic process in a pattern-forming system, namely RBC with periodic modulation of the Rayleigh number. The second set of experiments addresses questions for which stochastic effects play a negligible role. This is so when the pattern amplitude is so large and bifurcations are so far away that the perturbations due to noise can be ignored. The first topic in this category is an investigation of the band of stable states that exists above the first bifurcation in Taylor-vortex flow (TVF). The next issue is the selection of particular states out of this band by a spatial variation of the control parameter. It turns out that this selection is determined by the nature of the control-parameter variation, and not by the non-linear state as such. Thus, this experiment failed to provide any evidence for the existence of an extremum principle which might control the pattern-selection process. However, the results could be understood quantitatively in terms of theoretical models involving phase equations, and thus provide a welcome test of this theoretical approach well above the bifurcation where amplitude equations are no longer applicable. The third experiment in this category can be explained in terms of an amplitude equation, but requires complex coefficients. It involves the study of localized states, or pulses, of travelling convection rolls in a binary mixture. These pulses are related to the solitons in dispersive systems, but differ from them because of the dissipation in the hydrodynamic system. The equivalent of these pulses could not exist in a thermodynamic system, where the existence of a free energy would assure the survival of only one phase for a given set of intensive parameter values.
