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This application serves as a user-interactive animated visualization of the relativity of simultaneity as in the way explained by Hermann Bondi: distant events are established as simultaneous by some observer by radar pulses that are sent towards those events by the observer and reflected back to the observer each at the same time. The user of the application can adjust how far away the simultaneous events are from one of the observers (frame S), the relative velocity of the two observers, whether the animation's time represents the proper time of frame S or of S', whether or not the coordinate system S is mapped to S' and vice versa, and whether or not hyperbolas of constant proper time are displayed.
For more explanation and some mathematics, see this webpage.
To download this application (Java required for running), click here, unzip the file, and run the .jar file in the folder created. Note that the .jar file is unsigned (but is safe to run)---look up how to open unsigned .jar files on your OS to run it.