Rust designs and colors on steel sculpture

I've been making steel outdoor sculptures for several years. To avoid adding surface treatments that will only succumb to rust anyway, I leave some of my outdoor sculptures to rust nicely on their own.

I'd like to add some visual interest by adding brown, yellow or reddish color variation to the eventual rust by treating certain parts of the clean new steel piece with acid or some other chemical which will then change the color of the rust that develops over time?

What happens if I "paint" acid onto an already rusted piece?

I assume I can add a design on already rusted steel with phosphoric acid so that the design will turn black? Is it better to use only phosphoric acid or to use a commercial "rust converter ⇦ on eBay or Amazon [affil link] "? What is the purpose of the additional ingredients in commercial "rust converter ⇦ on eBay or Amazon [affil link] s"?