In a visual search experiment, the subject must find a target item hidden in a display of other items, and their performance is measured by their reaction time (RT). Here I look at how visual search reaction times are correlated with past reaction times. Target-absent RTs (i.e. RTs to displays that have no target) are strongly correlated with past target-absent RTs and, treated as a time series, have a 1/f power spectrum. Target-present RTs, on the other hand, are effectively uncorrelated with past RTs. A model for visual search is presented which generates search RTs with this pattern of correlations and power spectra. In the model, search is conducted by matching search items up with “categorizers,” which take a certain time to categorize each item as target or distractor; the RT is the sum of categorization times. The categorizers are drawn at random from a pool of active categorizers. After each search, some of the categorizers in the active pool are replaced with categorizers drawn from a larger population of unused categorizers. The categorizers that are not replaced are responsible for the RT correlations and the 1/f power spectrum.