  When one splits spacetime into space plus time, the spacetime curvature (Weyl
tensor) gets split into an "electric" part E_{jk} that describes tidal gravity
and a "magnetic" part B_{jk} that describes differential dragging of inertial
frames. We introduce tools for visualizing B_{jk} (frame-drag vortex lines,
their vorticity, and vortexes) and E_{jk} (tidal tendex lines, their tendicity,
and tendexes), and also visualizations of a black-hole horizon's (scalar)
vorticity and tendicity. We use these tools to elucidate the nonlinear dynamics
of curved spacetime in merging black-hole binaries.
