How are clusters from DBSCAN sometimes non-convex? I've been using clustering in my bag of ML techniques for quite some time now, and  I've never found a satisfying answer to this question.  

In DBSCAN, we define a maximum radius with which to form clusters.  The algorithm will scan the space and group together points that are ALL reachable from one another.  However, we can sometimes end up with a non-convex cluster.  

My confusion is around how the notion of a "radius", which describes a convex object, can be an input to an algorithm which results in a non-convex object?
A cluster in DBSCAN consists of multiple core points.

The radius is the area covered by a single core point, but together with neighbor core points the shape will be much more complex. In particular, they can be much larger than epsilon, so you should choose a small value, and rely on this "cover" functionality.

Wikipedia has an example of a non-convex cluster