Since you've tried multiple cables and various graphics solutions on different systems it does look like it may be a problem with the monitor itself. A few things I would check first would be that there is no possible interference between the monitor and other devices. The pattern you drew looks slightly like an interference pattern but this may be due to a monitor fault.
The best way to eliminate this, if the monitor is actually fine, would be to isolate the monitor as much as possible. Connect it up to your mac book in an area where there are no other nearby electronic devices (preferably no phones, routers, speakers etc.) and make sure the power cable is firmly connected into the monitor and anywhere else it needs to be connected. Make sure the monitor is as far away from the MacBook as possible. Also ensure that the power cable is the sole device connected to a particular power point when testing. If after this isolation the pattern can still be observed then it is most probably a fault with the monitor itself.
It is good that you like the monitor apart from that. It is a model that one of my colleagues is keen to recommend at the moment for overall price and performance but I haven't tested it myself. Testing or not that doesn't sound like something you should have to put up with and doesn't sound normal. Hope you can get it sorted!