Reason for seeing grid-like patterns when strobing a solid black-white image?
Seeing in animals is at some level using Gabor wavelets (Marčelja 1980 and later authors). Your images reminds of a combination of two low frequency Gabor basis vectors. Apparently the nervous system does not have time to model the incoming image into Gabor components of other frequencies. 

Here is a picture of two low frequency Gabor basis vectors added. (In this image rotated 45 degrees compared to your image.)
http://medicalxpress.com/news/2013-01-feature-combination-perceptual-identification.html

This is a signal processing or a linear algebra question as much as a biology question.

One could argue that even lower frequency Gabor vectors would model the original images even better.