The Web Roulette application has been released on the iPhone. It's not usually a browser: it's not confined the search for new information through Google or Yandex, and view your saved sites. Moreover, there is not even a search engine as such.
At the start, Web Roulette offers to select sites that you regularly visit. It is recommended to choose at least 10. The service offers a couple of dozen popular resources (though all in English), you can also add any of your own sites.
After that, you can open the Web Roulette every time you want to look through something without going into the wilds: you can only switch between selected sites (although no one forbids clicking on links from articles). It is suggested to scroll through the sites with swipes to the left, you can go back with a swipe to the right.
If you want to read something unexpected, just shake your smartphone: a random page from the Internet will open. For example, an article in Wikipedia about inventors who were killed by their own inventions. However, it will not work so often: the available "shakes" accumulate as you browse ordinary sites, so there is no risk of sticking to the watch, shaking the phone in search of something interesting.
The app is free and has no ads, it is available in the Russian App Store.