What's the meaning of "draw" in this context?

I'm reading one of Aesop's fables:

A CHARCOAL-BURNER carried on his trade in his own house. One day he met a friend, a Fuller, and entreated him to come and live with him, saying that they should be far better neighbors and that their housekeeping expenses would be lessened. The Fuller replied, "The arrangement is impossible as far as I am concerned, for whatever I should whiten, you would immediately blacken again with your charcoal."

Like will draw like.

What's the meaning of draw in the last sentence? I've checked the Oxford English dictionary but still cannot understand it.

Sense #5 of draw in Wiktionary is applicable: "To attract." An example given is: "I was drawn to her." Etymonline says this usage of the verb draw dates from the 1580s. For a different phrase with the same meaning, see birds of a feather flock together.

The meaning of draw in this context is specified here (definition 3). So, the phrase means this:

Things will attract similar things.