Faded red to dark purple with no bleaching?

Hello there.

I have this doubt since I've wanted to dye my hair purple. The thing is I don't want to bleach my hair due to its damage and because I'm mostly looking for a dark color and otherwise it becames really bright when it fades like happens to me now with the red.
I, unfortunately, live in a third world country and here we don't have too much options of brands to dye with so I don't care about it. I'm just focusing on the colors.

The type of dark purple I want is this one:

And now my hair is like this:

What do you say? Should I mix some blue since I have a redish base?
Also, if you know: What color tends to become when it fades?

Thanks a lot!