Algorithms and methods were developed to synthesize complex chemical waveforms in open volumes by using a scanning-probe microfluidic platform. Time-dependent variations and oscillations of one or several chemical species around the scanning probe, such as formation of sine waves, damped oscillations, and generation of more complex patterns, are demonstrated. Furthermore, we show that intricate bursting and chaotic calcium oscillations found in biological microdomains can be reproduced and that a biological cell can be used as a probe to study receptor functionalities as a function of exposure to time-dependent variations of receptor activators and inhibitors. Thus, the method allows for studies of biologically important oscillatory reactions. More generally, the system allows for detailed studies of complex time-varying chemical and physical phenomena in solution or at solution/surface interfaces.