Patterns in Grass

Years ago, Rick Beier asked if I had ever seen the grass patterns shown in the picture taken by Kevin Gerfin (below left).  Once seen the patterns are everywhere in the fall. On the morning of the first frost of the season, there is a very similar pattern of frost (below right). Evidently the grass turns brown where the frost appears and stays green where it is absent.  Why does the frost have a pattern?

The top surface of the grass radiates heat at night and cools relative to the ground below and the air above. The air near the warm ground is unstable to convection and begins moving upward like a helium balloon. This moving air is trapped between the ground below and air of the same temperature above. This produces convective rolls of a given size.  In a roll the air moves in a circle, up on one side and down on the other. The side with upward motion is slightly warmer than the side with downward motion.  As the average temperature drops to the frost point, frost forms on the colder side of the rolls.  The calculated size of the rolls, based on a fluid dynamics calculation, gives the distance between neighboring green zones above.