The internet is full of invisible borders—geographic, linguistic, cultural, political—that circumscribe the information each user sees. Search engines shape such “information borders” by tailoring results according to geolocation, language, and other user profiling. We present Search Atlas, a tool paired with visualizations that enable users to see and cross these borders. For instance, how do search results for the same query differ for Brazilian, Turkish, and Indian users? Given a query, the tool displays multiple lists of Google search results, highlighting distinctive words for each set of parameters. Then, we provide visu- alizations that juxtapose and cluster Google results across countries, revealing new information borders and regions that can vary widely depending on the query. By exposing the partial perspective of a search engine, Search Atlas invites users to experience the internet from divergent positions and to reflect on how their online lives are conditioned by technologi- cal infrastructures and geopolitical regimes.

Conceptual diagrams are used extensively to understand abstract relationships, explain complex ideas, and solve difficult problems. To illustrate concepts effectively, experts find appropriate visual representations and translate concepts into concrete shapes. This translation step is not supported explicitly by current diagramming tools. This paper investigates how domain experts create conceptual diagrams via semi-structured interviews with 18 participants from diverse backgrounds. Our participants create, adapt, and reuse visual representations using both sketches and digital tools. However, they had trouble using current diagramming tools to transition from sketches and reuse components from earlier diagrams. Our participants also expressed frustration with the slow feedback cycles and barriers to automation of their tools. Based on these results, we suggest four opportunities of diagramming tools — exploration support, representation salience, live engagement, and vocabulary correspondence — that together enable a natural diagramming experience. Finally, we discuss possibilities to leverage recent research advances to develop natural diagramming tools.

We introduce a system called Penrose for creating mathematical diagrams. Its basic functionality is to translate abstract statements written in familiar math-like notation into one or more possible visual representations. Rather than rely on a fixed library of visualization tools, the visual representation is user-defined in a constraint-based specification language; diagrams are then generated automatically via constrained numerical optimization. The system is user-extensible to many domains of mathematics, and is fast enough for iterative design exploration. In contrast to tools that specify diagrams via direct manipulation or low-level graphics programming, Penrose enables rapid creation and exploration of diagrams that faithfully preserve the underlying mathematical meaning. We demonstrate the effectiveness and generality of the system by showing how it can be used to illustrate a diverse set of concepts from mathematics and computer graphics.