As others have said, this is a moire pattern,
for which there are good references on the web such as the moire pattern wikipedia entry.
More specifically, the r,g,b contours you see are a shape moire (that is, a magnified distorted image) of the r,g,b scanlines of the computer screen in the photo.
The interesting part of this question to me is "why a saddle?", which I don't see answered elsewhere,
so that is what I'll investigate in this answer.
Why a saddle?
The OP's photograph looks to me like it has several different instances of the saddle phenomenon overlayed on each other, making it difficult to sort out what's going on.
So I took my own photograph of my computer screen using my phone's camera, and was able to get a cleaner view of what's happening, which I can inspect at the pixel level to see what these contours are really made of.
I included on the computer screen a small test pattern of fully saturated colors, to help identify which aspects of the picture were due to the computer screen and which were due to the camera.
Scrutinizing this photograph, what I see is, roughly, two grids:
- A luminance grid. This is the more-or-less rectangular grid of relatively bright spots
which make up the photo. I think of this grid as being the pixels of the photo or camera
(which is certainly a vast simplification of what's really going on).
- An rgb grid. This consists of more-or-less horizontal stripes of color in the photo. From bottom to top, the horizontal stripes are ordered red,green,blue,red,green,blue,... I think of these as the scan lines of the computer screen in the photo (again, this is a mental model that's a simplification of what's really going on).
The correspondence between the two grids is, of course, a perspective warp.
To get more of an idea of what this warp is like, we can inspect the photo some more,
and identify that, near the top-left of the picture, the almost-horizontal lines of the luminance grid
are sloping slightly downwards with respect to the rgb grid:
and near the bottom-left of the picture, they are sloping upwards instead:
So, roughly halfway between top and bottom, the slopes of the two grids' more-or-less-horizontal lines
have exactly the same slope, so the interference pattern seems to go away along that line.
This is the first point in the investigation that I can start to make out where the saddle shape is coming from: that horizontal line of stillness is in fact the horizontal "axis" of the saddle shape, at which
the interference behavior has slowed to zero and in fact reverses, in a sense.
And, evidently, there is a second reversal going on too: the other, more-or-less vertical, "axis" of the saddle.
What's going on there? The answer is that it's where the two grids have exactly the same spacing
between horizontal grid lines. To the left of that axis, the rows of pixels are spaced farther apart
than the rgb scanlines; to the right of that axis, they are closer together.
Okay, now maybe we have enough understanding to be able to recreate the phenomenon in a simulation.
Here is a picture of rgb scanlines, and another picture of a pixel grid.
Only one of the pictures needs to be perspective-warped with respect to the other,
so I chose to warp only the rgb scanlines.
I chose the warp in such a way as to recreate roughly the same arrangement as in the photo: that is,
- the top half of the picture has rgb scanlines sloping slightly upward with respect to the pixel rows,
the bottom half has them sloping slightly downward.
- the left half-or-so of the picture has pixel rows spaced more widely than the rgb scanlines,
and the right half-or-so has them spaced more tightly.
- the vertical-ish line that we expect to manifest as the vertical-ish axis of the saddle
is not exactly vertical, to keep it interesting.
When we overlay the two pictures, the saddle appears, as expected:
Inspection of the combined picture gives me a sense of why the contour lines have to go the way they do,
including the saddle shape showing where the two lines-of-reversal-of-behavior intersect.
The horizontal axis of the saddle is where the horizontal-ish lines of the two grids have the same slope,
and the vertical-ish axis of the saddle is where the horizontal-ish lines of the two grids have the same spacing.
Are they hyperbolas?
Notice that the same kind of saddle shape appears in the contour curves of mathematical functions such as $z = x y$; these saddle-shaped contour lines are hyperbolas.
The saddle shapes we see here are perspective warps of the contours of $z = x y$;
therefore they too are hyperbolas (or other conic sections such
as parabolas or elliptical arcs or circular arcs, but I don't see how those could manifest here).
In summary, saddle shapes (more specifically, hyperbolas) are what you get as colored contour lines of interference when a rectangular grid of pixels is overlayed on a picture of rgb scanlines such that the correspondence between the two pictures is a perspective warp, as is the case when you take a photograph of your computer screen with your phone.
The vertical grid lines don't matter
Actually, the vertical lines of the pixel grid don't matter; we can omit them
and the phenomenon still happens in full force. On the other hand, if we omit the horizontal lines
of the pixel grid, the phenomenon doesn't happen at all.