This paper examines the emergence of complex volatility in dynamic asset markets when there are heterogeneous agents. A discrete formulation is studied with two categories of market participants, fundamentalist traders who buy when the asset price is below the fundamental value and sell when it is above and noise traders who use moving average technical trading rules that can lead them to chase trends. Agents switch from one type of strategy to the other according to relative returns. A variety of outcomes are studied using numerical simulation, including variation of market price responsiveness to changes in excess demand, in switching behavior, and the introduction of noise. Bifurcation analysis of certain parameters is presented.