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Bacterial chemotaxis refers to the locomotory response of bacteria to chemical stimuli, where the general biological function is to increase exposure to some substances while reducing exposure to others. In this paper, we introduce an algorithm for surface mapping based on a model of the biological signaling network responsible for bacterial chemotaxis. The algorithm tracks the motion of a bacteria-like software agent, referred to as a bacterial agent, on an objective function. Results from simulations using one- and two-dimensional test functions show that the surface mapping algorithm produces an informative estimate of the surface, revealing some of its key characteristics. We also present a modification of the algorithm in which the software agent is given the ability to reduce the value of the surface at locations it visits (analogous to a bacterium consuming a substance as it moves in its environment) and show that it is more effective in reducing the surface integral within a certain period of time than a bacterial agent lacking the ability to sense surface information or respond to it.