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

Question

In the third page (the third paragraph in the right column) of the paper "Time, Clocks, and the Ordering of Events in a Distributed System" by Leslie Lamport, it says that

The reader may find it helpful to visualize a two-dimensional spatial network of processes, which yields a three-dimensional space-time diagram. Processes and messages are still represented by lines, but tick lines become two-dimensional surfaces.

However I failed to visualize them in my head, especially the two-dimensional surfaces. Could anyone make more explanations? An illustrative picture would be excellent.

Answer 1

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.