The Extraordinary Sky of Saddlestania

The infinite country of Saddlestania has some very interesting geography: its elevation from the mathematically flat sea level exactly follows the equation $$mathbf{z=x^2-y^2}.$$

After traveling along the infinitely long, yet perfectly straight coastline, you arrive at Saddle Point, the only place in the country where you can comfortably take a nap

so you lie down on your back to rest, and look straight up. What do you see?

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For the more rigorous-minded perspective ponderers, here’s the same puzzle without flavour:

If you plot the surface $z=x^2-y^2$ so that every line of sight that intersects the surface is green, and other lines of sight are white, what is the image you get when you place a camera at the origin (x=y=z=0) and point it up (along the positive z axis)?

_{^{This puzzle comes from a friend of mine (T. Lukka), who once forgot to set the camera parameters in the ray tracing software he was testing.}}