A possibility is redrawing the whole screen at each frame. For instance (only tested on linux):

#!/usr/bin/perl -w

# Array containing all lines
my @screen = ( ' 'x70 . "\n" ) x 20;

# Array of possible (equiprobable) characters
my @char = split //, '                     *|';

while(1) {
    print join '', @screen;
    # Drop last line
    pop @screen;
    # Put a new line on top
    unshift @screen, join ( '', map { $char[ rand(@char) ] } (1..70) )
+ . "\n";
    # Sleep for 0.1 seconds
    select(undef, undef, undef, 0.1);
}
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Update: The value 20 in the @screen initialization should be at least the terminal height minus 1 (due to the last line being empty). If it's less, then the upper portion of each frame is filled by the last lines of the previous one.