The author is developing a numerical code with thousands of emission zones to simulate the time-dependent multi-waveband emission from blazars. The code is based on a model in which turbulent plasma flowing at a relativistic speed down a jet crosses a standing conical collimation shock that accelerates electrons to maximum energies in the 5-100 GeV range. This paper reports early results produced by the model. The simulated light curves and time profiles of the degree and position angle of polarization have a number of features in common with the observational data of blazars. Maps of the polarized intensity structure can be compared with those of blazars observed with very long baseline interferometry at short millimeter wavelengths.