We have created “encoding manifolds” to reveal the overall responses of a brain area to a variety of stimuli. Encoding manifolds organize response properties globally: each point on an encoding manifold is a neuron, and nearby neurons respond similarly to the stimulus ensemble in time. We previously found, using a large stimulus ensemble including optic flows, that encoding manifolds for the retina were highly clustered, with each cluster corresponding to a different ganglion cell type. In contrast, the topology of the V1 manifold was continuous. Now, using responses of individual neurons from the Allen Institute Visual Coding–Neuropixels dataset in the mouse, we infer encoding manifolds for V1 and for five higher cortical visual areas (VISam, VISal, VISpm, VISlm, and VISrl). We show here that the encoding manifold topology computed only from responses to various grating stimuli is also continuous, not only for V1 but also for the higher visual areas, with smooth coordinates spanning it that include, among others, orientation selectivity and firing-rate magnitude. Surprisingly, the encoding manifold for gratings also provides information about natural scene responses. To investigate whether neurons respond more strongly to gratings or natural scenes, we plot the log ratio of natural scene responses to grating responses (mean firing rates) on the encoding manifold. This reveals a global coordinate axis organizing neurons’ preferences between these two stimuli. This coordinate is orthogonal (i.e., uncorrelated) to that organizing firing rate magnitudes in VISp. Analyzing layer responses, a preference for gratings is concentrated in layer 6, whereas preference for natural scenes tends to be higher in layers 2/3 and 4. We also find that preference for natural scenes dominates the responses of neurons that prefer low (0.02 cpd) and high (0.32 cpd) spatial frequencies, rather than intermediate ones (0.04 to 0.16 cpd). Conclusion: while gratings seem limited and natural scenes unconstrained, machine learning algorithms can reveal subtle relationships between them beyond linear techniques.