Flipboard-like iOS app for "reading" the whole web
You could make a Fluid app of Feedly and subscribe to completely random feeds so you're surprised by what turns up and/or even subscribe to the Pocket, Readability, etc. feeds of completely random people and/or the front page of Reddit. If you set Fluid to use Safari you can "flip" through the pages using the regular OS gestures. And Feedly allows you to choose from a variety of presentation modes. You could, also, do this with any desktop feed reader like Reeder 2, NetNewsWire, etc., but as far as I know creating a Feedly app with Fluid with Safari set as the browser may be the only way to "flip through pages" of completely random content.