Meaning of lines on x- and y-axis of a centered FFT-spectrum of an image

I am currently learning about the Fourier transform of digital images, but I am wondering about one aspect.
In most visualisations of fourier transforms of images, a horizontal and a vertical line in the middle seem to be rather dense compared to the rest of the image. Below is an image of two pattern which, from my understanding, should only have three entries in the fourier spectrum each.

That there are more than three lines should be due to the fact that there are horizontal and vertical sinusoidal waves of most frequencies used to represent the original image.
These two lines in the FFT-spectrum seem to appear in most images, not only in such with regular patterns, so my guess is it has something to do with the discrete pixels, but i can’t quite wrap my head around why it would use all frequencies and only in those two directions.
Even if it is about "sampling" the pixels, wouldn’t diagonal lines be as well suited to represent quadratic pixels (for less regular images than above)?