If a homogeneous illuminated test field is inserted within a sine-wave grating, an opposite phase grating will be perceived in the test field under a wide range of conditions. A cancellation technique was used to measure the magnitude of grating induction. The manner in which the effect depends on eye movements, inducing frequency, test-field height, inducing-field height, inducing amplitude, test-field luminance, and test-field width was determined in four experiments. Mathematical equations that describe these results are presented. It is shown that linear filters whose spatial weighting functions resemble receptive fields of the most common types of visual cell do not produce outputs with the properties of induced gratings. However, linear filters with highly elongated negative end zones and a small positive center produce opposite phase gratings in the test field, and an array of such filters of different sizes can account for several properties of induced gratings. There are other properties of the effect that are highly nonlinear. A second model, which is nonlinear and based on the properties of hypercomplex cells, is suggested that may encompass both the linear and the nonlinear properties of the effect.