purple: if you continue certain hatena services (ex. write diary 1000 days, entry haiku 1000 days etc.) you'll get one purple star each.
as appreciable green:if you answer valuable question and get selected as best answer you will get 2 green stars, or if you get points in answering you can change it to star box
自動翻訳でなんかアメリカ独立と国旗の話みたいになってますが
in addition green star could be get by doing hatena haiku 2 tutorial, but I don't know it be still now
So, you can't get these stars for free?