Lenses are characterized by their aberrations. Most people know about chromatic aberrations — the rainbow blur caused by the wavelength dependent index of refraction of the glass. Most people know about defocus, which just means that your focal plane is not in the right spot. Some of the others are spherical aberrations, field curvature, astigmatism and coma — as well as higher order terms. All of these degrade the image in different ways but the result is that it looks blurry. Most images you can’t tell by looking at the photo which aberrations are causing the problem (although if you’re using a commercial lens it’s probably defocus — or motion blur, but that isn’t an aberration so much as ataxia, — in other words human error).
What is of interest here is an aberration called distortion. Distortion is described with a simple formula that is a function of where the light passes through the pupil, where it’s coming from and the angle between those two vectors.
What is interesting about distortion is that it changes the image but doesn’t degrade it. Distorted images appear in focus, straight lines just bend. These pictures are distorted, just a little (look at the straight sidewalk at the bottom of the frame). Sometimes this is very bad (architectural photography) sometimes it’s okay to roll with it and pretend the curves are natural.