In one of the courses I’ve attended in coursera, design was defined as “conceiving or giving form to artifacts that solve problems.” Artifacts meant anything that was human made - products, hardware or software.
Ryan Singer, a designer at 37signals, explains this same concept a bit more:
People use your product because they are trying to get somewhere. You can imagine them standing in front of a chasm with their goal on the other side. They want to do something, but they can’t do it without help. Your product is there to bridge the gap.
So what do we see here - sometimes people feel there’s a gap in an existing experience and want to make it better. An artifact (or a ‘product’) is designed to offer the better experience.
Artistic expression is different from design in the sense that it may not necessarily solve a problem. It can just be a medium to communicate emotion or force viewers to ask questions.
So while creating your own custom ambigrams can be an artistic expression:
If you had used it to solve a particular problem (for instance a glass that can be flipped over and still show the same logo), you’d be designing a solution:
You’d be showing a consistent marketing logo & you’d have a memorable conversation piece for your customers.