Be aware there is an optical illusion taking place due to the shine of the metal making it possibly appear that there are 2 center points in the pattern. There aren't.
What follows is far from perfect I realize. I did not spend a great deal of time in order to precisely figure out blend steps and spacing. But this would achieve the pattern with relative ease. You just have to factor in distance and blend steps more than I took the time to do. In addition, working on much larger shapes helps the transitions a great deal. This answer is to show the overall technique not get you directly to a perfect solution. The end result will take refinement for each use case.
This is merely a blend using a dotted path (with 3 anchor points) and a semi circle with the same dotted path. For the center of the pattern you need a separate blend in order to control spacing.
(Note the straight path has 3 anchors. Just select the path and choose
Object > Path > Add Anchors to add a center anchor. It needs 3 anchors because the semi-circle has 3 anchors.)
To be honest, the longer the straight path is, the smoother the transition is going to be. For the sake of these screenshots I didn't extend the path as long as I actually would have. The path works better at about twice the length shown here.
Then you create a second blend for the center.
With this in place, you merely add a clipping mask to hide portions resulting in a final "circle: shape. If you need that actual center dot, add that manually.
Because of the transitions you can't really pull this off with a single blend. You get too many steps between the center and not enough on the outside. Not to mention the fact that blending a full circle to a straight path really makes one part of the blend "wonky" because it's got to move from the bottom anchor of the circle to be parallel with the other anchors.