We use a novel search task to investigate the spatial distribution of visual attention, developing a general model from the data. Observers distribute attention to locations defined by stripes with a high penalty for attention to intervening areas. Attended areas are defined by a square-wave grating. A target is in one of the even stripes, and ten false targets (identical to the real target) are in the odd stripes; the observer must attend the even stripes and strongly ignore the odd, reporting the location of the target. As the spatial frequency of the grating increases, performance declines. Variations on this task inform a model that incorporates stimulus input, a "low pass" attentional modulation transfer function, and an acuity function to produce a strength map from which the location with the highest strength is selected. A feature-strength map that adds to the attention map enables the model to predict the results of attention-cued conjunction search experiments, and internal noise enables it to predict the outcome of double-pass experiments and of variations in the number of false targets. The model predicted performance on a trial-by-trial basis for three observers, accounting for approximately 70% of the trials. Actual trial-to-trial variation for an observer, using the double-pass method, is about 76%. For any requested distribution of spatial attention, this general model makes a prediction of the actually achieved distribution.