X server

That section contains SOME useful information about X servers.

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What does :0.0 mean?

The :0.0 part of the DISPLAY variable denote the display and the screen of an X server.

The display is the first number and equals to a running instance of an X server. If it is using TCP/IP for communication it listens on port 6000 + display-number for connections. With local (UNIX domain sockets) it uses the socket /tmp/.X11-unix/Xdisplay-number

The screen denotes different output devices of the X server. You could start XWin.exe with two -screen options and would end up with two X11 windows. Each of them is a different screen. Other X servers open different screens for different monitors connected to the computer.

Cygwin/X supports different formats of the DISPLAY variable

:0.0 or unix:0.0
This names a local X server and the communication uses the UNIX domain sockets.

hostname:0.0
This names a remote X server and the communication uses the TCP/IP network.

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Cygwin:

Xlib: connection to "local_host_name_or_ip_address:0.0" refused by server Xlib: Maximum number of clients reached

Cygwin/X queries getdtablesize () for the maximum number of client connections allowed; by default Cygwin returns 32 from getdtablesize (). Cygwin/X Server Test Series release Test44, released on 2001-08-15, changes the maximum number of clients from 32 to 1024 by passing the square of getdtablesize () to setdtablesize ().

Solaris:

It's in the FAQ, naturally:
3.57) How can I have more than 128 X windows clients?
   When you get the following errors, you've run out of X sockets.
       Xlib: connection to :0.0 refused by server
       Xlib: maximum number of clients reached
   By default, the X server has a limit of just 128.  In order to
   increase this limit, you need to run at least Solaris 8 or an
   earlier release with the Xserver patch applies that fixes bug:
       4185418 the X server should support more connections
   Then change the Xservers configuration file and add the "-clients 1024"
   option to the X commandline.
Since I'm running Solaris 8, I can change max clients.