Generate Toothpick Sequence What is Toothpick Sequence?
According to Wikipedia

In geometry, the toothpick sequence is a sequence of 2-dimensional
patterns which can be formed by repeatedly adding line segments
(&quot;toothpicks&quot;) to the previous pattern in the sequence.
The first stage of the design is a single &quot;toothpick&quot;, or line
segment. Each stage after the first is formed by taking the previous
design and, for every exposed toothpick end, placing another toothpick
centered at a right angle on that end.
This process results in a pattern of growth in which the number of
segments at stage n oscillates with a fractal pattern between 0.45n2
and 0.67n2. If T(n) denotes the number of segments at stage n, then
values of n for which T(n)/n2 is near its maximum occur when n is near
a power of two, while the values for which it is near its minimum
occur near numbers that are approximately 1.43 times a power of two.
The structure of stages in the toothpick sequence often resemble the
T-square fractal, or the arrangement of cells in the Ulam–Warburton
cellular automaton.
All of the bounded regions surrounded by toothpicks in the pattern,
but not themselves crossed by toothpicks, must be squares or
rectangles. It has been conjectured that every open rectangle in the
toothpick pattern (that is, a rectangle that is completely surrounded
by toothpicks, but has no toothpick crossing its interior) has side
lengths and areas that are powers of two, with one of the side lengths
being at most two.

Task
You must make a program or function that take input from STDIN, function argument, or commandline argument and make a tootpick fractal at that stage. Leading and trailing newline is prohibited except if it is unavoidable. Bounding box must be at minimum, including leading and trailing space. For inital line, we make two \ diagonal in space. The input is guaranteed to be less than two thousand. At least one line have non-space character. Trailing space is allowed.
Test Cases
1
\ 
 \     

5
    \     
    /\    
   /\     
  / /\   
\/\/\ \ \ 
 \ \ \/\/\
    \/ /  
     \/   
    \/    
     \
CJam, 99 93 bytes

This got rather long...

"\ "_W%]{{Sf+W%z}4*2ew{2fewz{_sa"\//\\"4S**4/^_,3={:.e&gt;W%2/\}&amp;;}%z{\)a@.e&gt;+}:Ff*}%{F}*}q~(*N*


Test it here. If you want to test larger inputs, like the 89 on Wikipedia, Dennis's TryItOnline uses the much faster Java interpreter under the hood and can handle inputs like that in a few seconds.

I'm sure there is a lot of room for improvement, and I'll add an explanation once I'm happier with the score...

Here is the output for N = 13:

            \             
            /\            
           /\             
          / /\            
        \/\/\ \ \         
         \ \/\/\/\        
           /\/\/          
          / /\ \          
    \    /\/\ \     \     
    /\  /  \/\/\    /\    
   /\  /\  /\/  \ \/\     
  / /\/ /\/ /\  /\ \/\    
\/\/\/\/\/\/\ \/\ \/\ \ \ 
 \ \ \/\ \/\ \/\/\/\/\/\/\
    \/\ \/  \/ /\/ /\/ /  
     \/\ \  /\/  \/  \/   
    \/    \/\/\  /  \/    
     \     \ \/\/    \    
          \ \/ /          
          /\/\/           
        \/\/\/\ \         
         \ \ \/\/\        
            \/ /          
             \/           
            \/            
             \            


For my own reference when golfing this further, some other ideas:

"\ "_W%]{{Sf+W%z}4*2few2ew::.{+_a"\//\\"4S**4/^_,3={:.e&gt;W%\}&amp;;2/}:z{\)a@.e&gt;+}ff*{\)a@..e&gt;+}*}ri(*N*




"\ "_W%]{{Sf+W%z}4*2ew{2fewz{_sa"\//\\"4S**4/^_,3={:.e&gt;W%2/\}&amp;;}%{.{\)a@.e&gt;+}}*}%{\)a@.e&gt;+}*}q~(*N*