I am working on designing animal icons and was curious the best way to create a sheep icon. I am looking for the most efficient way to make the circles on the fur.
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Just make one circle and copy it along the perimeter of the sheep. – Janus Bahs Jacquet Jul 22 '17 at 8:29
It may be too late for you, but to expand on the concept of copying circles along the sheep's perimeter, I created a partial one for demonstration purposes.
First I drew the overall sheep using the vector tool. I inset the wooly bits some so there'd be room for the circles.
Then I created an oval and positioned one in place. I then duplicated it (option-dragged the outline), rotated it (command-dragged a corner), and resized it (option-dragged an edge for mirrored resizing to simplify things) until it fit. Repeat the process until you've created them all. (In one case I edited an oval in vector mode because a "pure" oval wouldn't mimic the original.)
Then I selected everything and combined the shapes as a "union" (Layer > Combine > Union, or the Union button in the toolbar).
It's a bit time-consuming, but not bad. Though I obviously didn't create all of the ovals, the part that I did do took about 20 minutes (yes, I'm avoiding real work).
Create the rough outline for the fur first. In Object > Path > Add anchor points, add as many anchor points as you want which will serve to create the curves for the fur. Then in Effect > Distort & Transform > Pucker & bloat, add some bloating. You should get something similar to this: