Draw the Hilbert Curve
MATL, 39 38 bytes
O5:&quot;tZjJ*JQ-wJq+t2+&amp;y2j+_v2/]XG25Y01ZG

This takes the number of iterations as input. If you want to hard-code it, replace i by the number.
The program is a port of the Matlab code by Jonas Lundgren shown here.
The result is shown below. You can also try it at MATL Online! It takes a couple of seconds to produce the output. This compiler is experimental; you may need to refresh the page and press &quot;Run&quot; again if it doesn't initially work.

Explanation
O          % Push 0. This is the initial value of &quot;z&quot; in the original code
5:&quot;        % Do 5 times
  t        %   Duplicate
  Zj       %   Complex conjugate
  J*       %   Multiply by 1j (imaginary unit). This is &quot;w&quot; in the original code
  JQ-      %   Subtract 1+1j
  w        %   Swap: brings copy of &quot;z&quot; to top
  Jq+      %   Add 1-1j
  t        %   Duplicate
  2+       %   Add 2
  &amp;y       %   Duplicate the third element from top
  2j+_     %   Add 2j and negate
  v        %   Concatenate the three matrices vertically
  2/       %   Divide by 2
]          % End
XG         % Plot (in complex plane). The numbers are joined by straight lines
25Y0       % Push string 'square'
1ZG        % Make axis square