Most of DeviantArt's searching and browsing capabilities are exposed through RSS. Specifically, we support Media RSS.
Here is an example query, searching for the term frogs, ordered by all-time popularity, in the digital art/drawings category:
https://backend.deviantart.com/rss.xml?type=deviation&q=boost%3Apopular+in%3Adigitalart%2Fdrawings+frogs
And here's the feed of newest deviations by artist spyed:
https://backend.deviantart.com/rss.xml?type=deviation&q=by%3Aspyed+sort%3Atime+meta%3Aall