Is this right?
 

I am trying to put up a piece of fan art in Japanese but I was wondering if this was written right?

私 は 本当 の 目的 の ため の この 芸術 を しな かった

What I wanted to say is:

I had done this art for no real purpose

[As in being silly, if that helps.]

Thanks in advance.

It is a nice try. The most awkward part is 目的 の ため の この. That is at least one too many の there.

To use as much as what you used, maybe something like:

「本当の目的があってこの芸術をしたわけではない。」

I took the liberty of deleting the pronoun because it sounds better that way.