Visualization of Lamport's three-dimensional "space-time diagram" with introduced "tick lines"
Here's my take:

...and here's a 3D version without the nice colors.

Vertical black lines are processes; magenta lines are messages (wavy lines); spheres are events, and time is on the vertical (blue) axis.  The planes are 'tick lines.'  

In Dr. Lamport's original diagrams, messages are only passed between "adjacent" processes.  Presumably in a real distributed system any process can send a message to any other process, but this is hard to draw clearly in a 2D diagram.