Why looks the Moire pattern on my screen like the contour plot of z = xy?

graphing-functions

The reason is due to slight mismatch of two coordinate systems. For a simple example, suppose we have the usual Cartesian coordinate system and another affine coordinate systems which is slightly off. That is, the points with coordinates $(0,0), (1,0), (0,1)$ are mapped to the same points but the point with coordinates $(1,1)$ is mapped to the point $(1+t,1+t)$ where $t$ is small. But now, the point with coordinates $(x,y)$ is mapped to the point $(x+xyt,y+xyt)$. The point with coordinates $(x,y$) is mapped to $(a+bx+cy+dxy,e+fx+gy+hxy)$ in the most general affine mapping and even more complicated in a general projective mapping, but I deliberately chose a very simple case.

The difference in coordinates is $(xyt,xyt)$. If we assume that $xyt$ is a small fixed quantity based on screen resolution, then $x$ and $y$ are inversely proportional which explains the similarity to a $z=xy$ contour plot.

The photo taken was slightly tilted and not strictly parallel to the plane of the screen. The actual situation here is more complicated due to real world effects such as projective mappings than the simple example I gave, but it essentially has similar features and similar moire effects. This is no "physical effect" but a mathematical and geometrical one as I will now demonstrate.

I tested this effect with some Wolfram Mathematica code:

wc[p1_, w1_, p2_, w2_] := (p1*w1 + p2*w2)/(w1 + w2);
VGrid[L1_, L2_, n_: 1] := 
  Table[Line[{wc[L1[[1]], i, L1[[2]], n - i], 
  wc[L2[[1]], i, L2[[2]], n - i]}], {i, 0, n}];
HGrid[L1_, L2_, n_: 1] := 
  Table[Line[{wc[L1[[1]], i, L2[[1]], n - i], 
  wc[L1[[2]], i, L2[[2]], n - i]}], {i, 0, n}];
HVGrid[L1_, L2_, n_: 1, m_: 1] := 
  Join[VGrid[L1, L2, n], HGrid[L1, L2, m]];

With[{M=60, p1={0, 0}, p2={1, 0}, p3={0, 1}, p4={1, 1}},   
  Graphics[Join[HVGrid[{p1, p2}, {p3, p4}, M, M],
  HVGrid[{p1, p2}, {p3, p4 (1-9/M)}, M, M]], ImageSize->300]]

You can try it yourself at Wolfram Development Platform by creating a new notebook. The Moire pattern image with $t=-9/60$ is this:

Moire pattern