Mark,I hate to tell you but that's just not true. The height of the fairways, particularly tournament courses is exactly the same from tee to green and the same from hole to hole. The rough may be mowed at different hieghts, but the fairways and greens are uniform.
That linear or checkerboard affect is created by the type of mower they use. The typical lawn mower is a rotary blade. However, Golf Course maintenance uses a Reel Blade Mower. It's similar to the old push mower that had blades on a reel around the axle of the mower. The affect of the Reel Blade is to push the cut blades in one direction. That's what is generally called "Grain" in GolfSpeak. The mowers travers the fairway, alternating direction and thus the affect is born. It's not the hieght that gives the look, rather the difference ton blade laying toward the viewer rather than away from the viewer. It's that slight reflection from the sun or light source.
I spent nearly half my year for over twenty years on Golf Courses and watched in a demotion how the grounds crews prepared the various courses for play. I also was aware that two balls in the fairway might have vastly different lies, not due to grass height, necessarily, but because one ball sitting with the grain might be slightly easier to hit than a ball sitting against the grain. It was always just a little easier to spin the ball with the grain than against it.
Hope that helps.