The Santa Fe Artificial Stock Market consists of a central computational market and a number of artificially intelligent agents. The agents choose between investing in a stock and leaving their money in the bank, which pays a fixed interest rate. The stock pays a stochastic dividend and has a price which fluctuates according to agent demand. The agents make their investment decisions by attempting to forecast the future return on the stock, using genetic algorithms to generate, test, and evolve predictive rules. The artificial market shows two distinct regimes of behavior, depending on parameter settings and initial conditions. One regime corresponds to the theoretically predicted rational expectations behavior, with low overall trading volume, uncorrelated price series, and no possibility of technical trading. The other regime is more complex, and corresponds to realistic market behavior, with high trading volume, high intermittent volatility (including GARCH behavior), bubbles and crashes, and the presence of technical trading. One parameter that can be used to control the regime is the exploration rate, which governs how rapidly the agents explore new hypotheses with their genetic algorithms. At a low exploration rate the market settles into the rational expectations equilibrium. At a high exploration rate it falls into the more realistic complex regime. The transition is fairly sharp, but close to the boundary the outcome depends on the agents’ initial “beliefs”—if they believe in rational expectations they occur and are a local attractor; otherwise the market evolves into the complex regime.