According to the Wikipedia article on anisogamy, some types of this form of sexual reproduction involve motile egg cells, i.e. they're capable of movement under their own power, just like sperm cells.
Is the "egg cells can be motile" part true? If so, what examples of anisogamous species exhibit this? Because this could have tremendous implications on how to define "male" and "female"; having motile egg cells means that you could have a hypothetical species in which it's the female that "inseminates" the male with her gamete(s), with the sexes being assigned based on which gamete absorbs the other as in oogamous reproduction.