Contrails don’t form regular rectangular grids in the sky with the lines at perfect right angles to each other, evenly spaced. There’s something else going on, above and beyond the occurrence of normal contrails. I grew up next to an airport and what is in these photos is not what I used to see from airplanes.
Yes, they can form very regular patterns. It all depends on the flight pattern of the jets that form the contrails (stating the obvious). In fact, because most jets take off the same direction, it is very normal for there to be parallel sets of contrails. In order for a third or fourth contrail to cross the takeoff contrails at a 90-degrees angle, all you would need to do is to have a jet at a higher elevation (and not having taken off from the airport in question) cross at that angle. Keep in mind that the contrails may or may not be at the same altitude...they just appear that way.
Have you ever noticed that on some days there are a lack of contrails in the sky? This would happen during warmer weather when the atmosphere is not cold and there is low humidity. So why would the government not want to spray on those days?
Also, if you were to track the jets leaving an airport, you would probably see that they are responsible for the vast majority of contrails. As you probably know, commercial airlines take great pains to get rid of every pound of weight possible. Because every reduction in weight makes it less expensive to raise the jet and its cargo to about seven miles in the sky. So if the government were to have them spray us all with whatever, it would be a fairly expensive proposition. And why would the airlines (or the government, for that matter) be interested in spraying us with whatever? I worked for an airline manufacturer for over 30 years and never, ever heard any discussion or saw anything in any airplane that would make me think there was some kind of chemtail system installed on the airplane.
Anyway, I hope this eases your mind about contrails vs. chemtrails. It is my strong opinion that it is just a conspiracy theory that needs to die.