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The dash pattern (dashtype) is a separate property associated with each line, analogous to linecolor or linewidth. It is not necessary to place the current terminal in a special mode just to draw dashed lines. I.e. the old command set term <termname> {solid|dashed} is now ignored.
All lines have the property dashtype solid unless you specify otherwise. You can change the default for a particular linetype using the command set linetype so that it affects all subsequent commands, or you can include the desired dashtype as part of the plot or other command.
Syntax:
      dashtype N          # predefined dashtype invoked by number
      dashtype "pattern"  # string containing a combination of the characters
                          # dot (.) hyphen (-) underscore(_) and space.
      dashtype (s1,e1,s2,e2,s3,e3,s4,e4)  # dash pattern specified by 1 to 4
                          # numerical pairs <solid length>, <emptyspace length>
Example:
      # Two functions using linetype 1 but distinguished by dashtype
      plot f1(x) with lines lt 1 dt solid, f2(x) with lines lt 1 dt 3
Some terminals support user-defined dash patterns in addition to whatever set of predefined dash patterns they offer.
Examples:
     plot f(x) dt 3            # use terminal-specific dash pattern 3
     plot f(x) dt ".. "        # construct a dash pattern on the spot
     plot f(x) dt (2,5,2,15)   # numerical representation of the same pattern
     set dashtype 11 (2,4,4,7) # define new dashtype to be called by index
     plot f(x) dt 11           # plot using our new dashtype
If you specify a dash pattern using a string the program will convert this to a sequence of <solid>,<empty> pairs. Dot "." becomes (2,5), dash "-" becomes (10,10), underscore "_" becomes (20,10), and each space character " " adds 10 to the previous <empty> value. The command show dashtype will show both the original string and the converted numerical sequence.