26
\$\begingroup\$

Introduction

The Dragon's Curve is a fractal curve that notably appears on section title pages of the Jurassic Park novel.

It can very simply be described as a process of folding a paper strip, as explained in the Wikipedia article about this curve.

The first few iterations of the generation of this curve look like this (credits to Wikipedia for the image):

enter image description here

The challenge

Write a program or function that, given an integer n as input, outputs the n-th iteration of the dragon curve as ASCII art using only the symbols _ and |

  • You have to output the figure using only |, _ and spaces. You may not output the curve as a plot or anything else.
  • You can take the input as a program argument, in STDIN or as a function parameter.
  • Inputs will always be an integer >= 0. Your program should work for reasonable values of inputs, 12 being the highest in the test cases offered.
  • The first iterations shall look like this

    • Iteration 0 is

      _
      
    • Iteration 1 is

      _|
      
    • Iteration 2 is

      |_ 
       _|
      
  • One trailing line at the end is ok. No trailing spaces allowed besides filling the line up to the rightmost character in the curve

  • No standard loopholes abuse as usual

Test Cases

  • Input 0

Output

_
  • Input 3

Output

   _   
|_| |_ 
     _|
  • Input 5

Output

     _   _   
    |_|_| |_ 
 _   _|    _|
|_|_|_       
  |_|_|      
    |_       
     _|      
  |_|        
  • Input 10

Output

           _       _                                           
         _|_|    _|_|                                          
        |_|_   _|_|_   _                                       
         _|_|_| |_| |_|_|                                      
   _    |_|_|_        |_                                       
 _|_|    _| |_|        _|                                      
|_|_   _|_          |_|                                        
 _|_|_|_|_|_                                                   
|_| |_|_|_|_|_                                                 
     _|_|_| |_|                                                
    |_| |_                                                     
         _|_   _   _           _   _           _   _           
   _    |_|_|_|_|_|_|_        |_|_|_|_        |_|_|_|_         
 _|_|    _|_|_|_|_| |_|    _   _|_| |_|    _   _|_| |_|        
|_|_   _|_|_|_|_|_        |_|_|_|_        |_|_|_|_             
 _|_|_|_|_|_|_|_|_|_   _   _|_|_|_|_   _   _|_|_|_|_   _   _   
|_| |_|_|_| |_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_ 
     _|_|    _|_|    _|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|
    |_|     |_|     |_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_     
                         _|_|_|_|_|_|_|_|_|_|_| |_| |_|_|_|_   
                   _    |_|_|_|_|_|_|_|_|_|_|_        |_|_|_|_ 
                 _|_|    _|_|_|_|_|_|_|_|_| |_|    _   _|_| |_|
                |_|_   _|_|_|_|_|_|_|_|_|_        |_|_|_|_     
                 _|_|_|_|_|_|_|_|_|_|_|_|_|_        |_| |_|    
                |_| |_|_|_| |_|_|_| |_|_|_|_|_                 
                     _|_|    _|_|    _|_|_| |_|                
                    |_|     |_|     |_| |_                     
                                         _|_   _   _           
                                   _    |_|_|_|_|_|_|_         
                                 _|_|    _|_|_|_|_| |_|        
                                |_|_   _|_|_|_|_|_             
                                 _|_|_|_|_|_|_|_|_|_   _   _   
                                |_| |_|_|_|_|_|_|_|_|_|_|_|_|_ 
                                     _|_|_|_|_|_|_|_|_|_|_| |_|
                                    |_| |_|_|_|_|_|_|_|_|_     
               _   _                     _|_|_| |_| |_|_|_|_   
              |_|_| |_             _    |_|_|_        |_|_|_|_ 
           _   _|    _|          _|_|    _| |_|    _   _|_| |_|
          |_|_|_                |_|_   _|_        |_|_|_|_     
            |_|_|                _|_|_|_|_|_        |_| |_|    
              |_   _       _    |_|_|_|_|_|_|_                 
           _   _|_|_|    _|_|    _|_|_|_|_| |_|                
          |_|_|_|_|_   _|_|_   _|_|_|_|_|_                     
            |_| |_| |_|_|_|_|_| |_| |_|_|_|_                   
                      |_|_|_|_        |_|_|_|_                 
                   _   _|_| |_|    _   _|_| |_|                
                  |_|_|_|_        |_|_|_|_                     
                    |_| |_|         |_| |_|                    
  • Input 12

Output

                                                               _   _           _   _                                           _   _           _   _                                           
                                                              |_|_|_|_        |_|_|_|_                                        |_|_|_|_        |_|_|_|_                                         
                                                           _   _|_| |_|    _   _|_| |_|                                    _   _|_| |_|    _   _|_| |_|                                        
                                                          |_|_|_|_        |_|_|_|_                                        |_|_|_|_        |_|_|_|_                                             
                                                            |_|_|_|_   _   _|_|_|_|_   _   _                                |_|_|_|_   _   _|_|_|_|_   _   _                                   
                                                              |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_                                |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_                                 
                                                           _   _|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|                            _   _|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|                                
                                                          |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_                                |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_                                     
                                               _   _        |_|_|_|_|_|_|_|_|_| |_| |_|_|_|_                   _   _        |_|_|_|_|_|_|_|_|_| |_| |_|_|_|_                                   
                                              |_|_|_|_        |_|_|_|_|_|_|_|_        |_|_|_|_                |_|_|_|_        |_|_|_|_|_|_|_|_        |_|_|_|_                                 
                                           _   _|_| |_|    _   _|_|_|_|_|_| |_|    _   _|_| |_|            _   _|_| |_|    _   _|_|_|_|_|_| |_|    _   _|_| |_|                                
                                          |_|_|_|_        |_|_|_|_|_|_|_|_        |_|_|_|_                |_|_|_|_        |_|_|_|_|_|_|_|_        |_|_|_|_                                     
                                            |_|_|_|_   _   _|_|_|_|_|_|_|_|_        |_| |_|                 |_|_|_|_   _   _|_|_|_|_|_|_|_|_        |_| |_|                                    
                                              |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_                                |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_                                                 
                                           _   _|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|                            _   _|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|                                                
                                          |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_                                |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_                                                     
                                            |_| |_| |_|_|_|_|_|_|_|_|_|_|_|_   _   _           _   _        |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_   _   _           _   _           _   _           
                                                      |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_        |_|_|_|_        |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_        |_|_|_|_        |_|_|_|_         
                                                   _   _|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|    _   _|_| |_|    _   _|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|    _   _|_| |_|    _   _|_| |_|        
                                                  |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_        |_|_|_|_        |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_        |_|_|_|_        |_|_|_|_             
                                                    |_| |_| |_|_|_|_|_|_|_|_|_|_|_|_   _   _|_|_|_|_   _   _|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_   _   _|_|_|_|_   _   _|_|_|_|_   _   _   
                                                              |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_| |_|_|_|_|_|_|_|_|_|_|_| |_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_ 
                                                           _   _|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|    _|_|    _|_|_|_|_|_|_|_|_|_|    _|_|    _|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|
                                                          |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_    |_|     |_| |_|_|_|_|_|_|_|_    |_|     |_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_     
                                               _   _        |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|                _|_|_|_|_|_|_|_|                _|_|_|_|_|_|_|_|_|_|_| |_| |_|_|_|_   
                                              |_|_|_|_        |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_           _    |_|_|_|_|_| |_|_           _    |_|_|_|_|_|_|_|_|_|_|_        |_|_|_|_ 
                                           _   _|_| |_|    _   _|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|    _|_|        _|_|    _|_|_|_|    _|_|        _|_|    _|_|_|_|_|_|_|_|_| |_|    _   _|_| |_|
                                          |_|_|_|_        |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_    |_|         |_|_   _|_|_|_|_    |_|         |_|_   _|_|_|_|_|_|_|_|_|_        |_|_|_|_     
                                            |_|_|_|_   _   _|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|                _|_|_|_|_|_|_|_|                _|_|_|_|_|_|_|_|_|_|_|_|_|_        |_| |_|    
                                              |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_   _            |_| |_|_|_| |_|_                |_| |_|_|_| |_|_|_| |_|_|_|_|_                 
                                           _   _|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|                _|_|    _|_|                    _|_|    _|_|    _|_|_| |_|                
                                          |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_   _            |_|     |_|                     |_|     |_|     |_| |_                     
                                            |_| |_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|                                                                _|_   _   _           
                                                      |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_                                                           _    |_|_|_|_|_|_|_         
                                                   _   _|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|    _|_|                                                        _|_|    _|_|_|_|_| |_|        
                                                  |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_    |_|                                                         |_|_   _|_|_|_|_|_             
                                                    |_| |_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|                                                                _|_|_|_|_|_|_|_|_|_   _   _   
           _       _                                          |_|_|_|_|_|_| |_|_|_| |_|_|_|_|_|_   _                                                            |_| |_|_|_|_|_|_|_|_|_|_|_|_|_ 
         _|_|    _|_|                                      _   _|_|_|_|_|    _|_|    _|_|_|_|_|_|_|_|                                                                _|_|_|_|_|_|_|_|_|_|_| |_|
        |_|_   _|_|_   _                                  |_|_|_|_|_|_|_    |_|     |_| |_|_|_|_|_|_   _                                                            |_| |_|_|_|_|_|_|_|_|_     
         _|_|_| |_| |_|_|                      _   _        |_|_|_|_|_|_|                _|_|_|_|_|_|_|_|                                      _   _                     _|_|_| |_| |_|_|_|_   
   _    |_|_|_        |_                      |_|_|_|_        |_|_| |_|_           _    |_|_|_|_|_| |_|_                                      |_|_| |_             _    |_|_|_        |_|_|_|_ 
 _|_|    _| |_|        _|                  _   _|_| |_|    _   _|    _|_|        _|_|    _|_|_|_|    _|_|                                  _   _|    _|          _|_|    _| |_|    _   _|_| |_|
|_|_   _|_          |_|                   |_|_|_|_        |_|_|_    |_|         |_|_   _|_|_|_|_    |_|                                   |_|_|_                |_|_   _|_        |_|_|_|_     
 _|_|_|_|_|_                                |_|_|_|_   _   _|_|_|                _|_|_|_|_|_|_|_|                                           |_|_|                _|_|_|_|_|_        |_| |_|    
|_| |_|_|_|_|_                                |_|_|_|_|_|_|_|_|_   _            |_| |_|_|_| |_|_                                              |_   _       _    |_|_|_|_|_|_|_                 
     _|_|_| |_|                            _   _|_|_|_|_|_|_|_|_|_|_|                _|_|    _|_|                                          _   _|_|_|    _|_|    _|_|_|_|_| |_|                
    |_| |_                                |_|_|_|_|_|_|_|_|_|_|_|_|_   _            |_|     |_|                                           |_|_|_|_|_   _|_|_   _|_|_|_|_|_                     
         _|_   _   _           _   _        |_|_|_|_|_|_|_|_|_|_|_|_|_|_|                                                                   |_| |_| |_|_|_|_|_| |_| |_|_|_|_                   
   _    |_|_|_|_|_|_|_        |_|_|_|_        |_|_|_|_|_|_|_|_|_|_| |_|_                                                                              |_|_|_|_        |_|_|_|_                 
 _|_|    _|_|_|_|_| |_|    _   _|_| |_|    _   _|_|_|_|_|_|_|_|_|    _|_|                                                                          _   _|_| |_|    _   _|_| |_|                
|_|_   _|_|_|_|_|_        |_|_|_|_        |_|_|_|_|_|_|_|_|_|_|_    |_|                                                                           |_|_|_|_        |_|_|_|_                     
 _|_|_|_|_|_|_|_|_|_   _   _|_|_|_|_   _   _|_|_|_|_|_|_|_|_|_|_|                                                                                   |_| |_|         |_| |_|                    
|_| |_|_|_| |_|_|_| |_|_|_|_|_|_|_|_|_|_|_| |_|_|_| |_|_|_|_|_|_   _                                                                                                                           
     _|_|    _|_|    _|_|_|_|_|_|_|_|_|_|    _|_|    _|_|_|_|_|_|_|_|                                                                                                                          
    |_|     |_|     |_| |_|_|_|_|_|_|_|_    |_|     |_| |_|_|_|_|_|_   _                                                                                                                       
                         _|_|_|_|_|_|_|_|                _|_|_|_|_|_|_|_|                                                                                                                      
                   _    |_|_|_|_|_| |_|_           _    |_|_|_|_|_| |_|_                                                                                                                       
                 _|_|    _|_|_|_|    _|_|        _|_|    _|_|_|_|    _|_|                                                                                                                      
                |_|_   _|_|_|_|_    |_|         |_|_   _|_|_|_|_    |_|                                                                                                                        
                 _|_|_|_|_|_|_|_|                _|_|_|_|_|_|_|_|                                                                                                                              
                |_| |_|_|_| |_|_                |_| |_|_|_| |_|_                                                                                                                               
                     _|_|    _|_|                    _|_|    _|_|                                                                                                                              
                    |_|     |_|                     |_|     |_|                                                                                                                                

Scoring

This is , so the shortest program in bytes wins.

\$\endgroup\$
  • \$\begingroup\$ I'm sure someone will complain about the vagueness of a 'huge amount of spaces', so how about an asymptotic bound? \$\endgroup\$ – feersum Jul 12 '15 at 9:52
  • 1
    \$\begingroup\$ @feersum Well I disallowed trailing spaces altogether, so nobody will complain now! \$\endgroup\$ – Fatalize Jul 12 '15 at 9:57
  • 2
    \$\begingroup\$ I'm complaining... now you're being a whitespace Nazi! \$\endgroup\$ – feersum Jul 12 '15 at 10:21
  • \$\begingroup\$ @feersum and you are a horizontal ellipsis Nazi! \$\endgroup\$ – Optimizer Jul 12 '15 at 12:35
  • \$\begingroup\$ This is the best fractal question ever, I hope I have time to participate! Is it ok to rotate the curve through 90,180,270 degrees or does it have to be displayed per the examples? \$\endgroup\$ – Level River St Jul 12 '15 at 13:00
9
\$\begingroup\$

Ruby, 239 201 bytes

This is a lambda function which should be called in the same manner as the one in the ungolfed version.

Golfing improvements include: assignment of 8<<n/2 to a variable for re-use; upto loop instead of each loop; ternary operator instead of if..else..end; use of [y,y+=d].max to calculate where to print the |; use of ?_ and ?| instead of the equivalent '|'and '_'; and elimination of redundant %4 (thanks Sp3000.)

->n{a=Array.new(m=8<<n/2){" "*m}
p=q=1+x=y=m/2
r=3
1.upto(1<<n){|i|d=(r&2)-1
r%2>0?(a[y][x+=d]=?_
x+=d):(a[[y,y+=d].max][x]=?|
p=x<p ?x:p
q=x>q ?x:q)
r+=i/(i&-i)}
a.delete(a[0])
puts a.map{|e|e[p..q]}}

It relies on the following formula from Wikipedia:

First, express n in the form k*(2^m) where k is an odd number. The direction of the nth turn is determined by k mod 4 i.e. the remainder left when k is divided by 4. If k mod 4 is 1 then the nth turn is R; if k mod 4 is 3 then the nth turn is L.

Wikipedia gives the following code:

There is a simple one line non-recursive method of implementing the above k mod 4 method of finding the turn direction in code. Treating turn n as a binary number, calculate the following boolean value: bool turn = (((n & −n) << 1) & n) != 0

I improved this to i/(i&-i)%4 which uses the same technique of using the expression i&-i to find the least significant digit but my expression gives 1 (for left turn)or 3 (for right turn) directly, which is handy as I track direction as a number 0..3 (in order north, west, south, east for golfing reasons.)

Ungolfed original in test program

f=->n{
  a=Array.new(8<<n/2){" "*(8<<n/2)}  #Make an array of strings of spaces of appropriate size 
  p=q=1+x=y=4<<n/2                   #set x&y to the middle of the array, p&q to the place where the underscore for n=0 will be printed.                             
  r=3                                #direction pointer, headed East
  (1..1<<n).each{|i|                 #all elements, starting at 1
    d=(r&2)-1                          #d is +1 for East and South, -1 for West and North
    if r%2>0                           #if horizontal
      a[y][x+=d]='_'                     #move cursor 1 position in direction d, print underscore,
      x+=d                               #and move again.
    else                               #else vertical
      a[(y+([d,0].max))][x]='|'          #draw | on the same line if d negative, line below if d positive
      y+=d                               #move cursor
      p=x<p ?x:p                         #update minimum and maximum x values for whitespace truncation later
      q=x>q ?x:q                         #(must be done for vertical bars, to avoid unnecesary space in n=0 case)
    end
    r=(r+i/(i&-i))%4                   #update direction
  }
  a.delete(a[0])                     #first line of a is blank. delete all blank lines.
  puts a.map!{|e|e[p..q]}                 #use p and q to truncate all strings to avoid unnecessary whitespace to left and right.
}


f.call(0)
f.call(2)
f.call(3)
f.call(11)
\$\endgroup\$
  • \$\begingroup\$ @Fatalize both functions are (currently) identical (except for the comments and whitespace.) I've added printing to stdout instead of returning a value (+5 bytes) and deleted the f= at the beginning as this is not normally counted for an anonymous function definition (-2 bytes.) More golfing tomorrow. Note that you will still have to execute the golfed function, by assigning it to a variable f=->n{.....} and calling it using f.call(n) as in the test program example. \$\endgroup\$ – Level River St Jul 13 '15 at 21:30
  • 1
    \$\begingroup\$ @Fatalize BTW I think the fractal looks absolutely awesome in my console. Thanks for the challenge. \$\endgroup\$ – Level River St Jul 13 '15 at 21:32
  • \$\begingroup\$ @Sp3000 indeed %4 is not necessary, as r is only used in the expressions r%2 and r&2. Thanks for the tip. I'm now down to 202. \$\endgroup\$ – Level River St Jul 14 '15 at 22:16
8
\$\begingroup\$

Python 2, 270 222 bytes

y=X=Y=0
i=m=x=1
D={}
k=2**input()
while~k+i:j=Y+(y>0);s={2*X+x};D[j]=D.get(j,s)|s;m=min(m,*s);Y+=y;X+=x;exec i/(i&-i)*"x,y=y,-x;";i+=1
for r in sorted(D):print"".join(" | _"[(n in D[r])+n%2*2]for n in range(m,max(D[r])+1))

Now using the formula for the nth turn. I saw the (((n & −n) << 1) & n) formula on Wikipedia, but didn't realise how useful it was until I saw it in @steveverrill's answer. I actually drop the %4 as well, so there's a lot of rotating going on, making larger inputs take a while.


Side remark: This isn't graphical output, but here's some golfed turtle code:

from turtle import*
for i in range(1,2**input()+1):fd(5);lt(i/(i&-i)*90)
\$\endgroup\$
  • \$\begingroup\$ As long as it doesn't take an hour to run, it's fine by me \$\endgroup\$ – Fatalize Jul 12 '15 at 15:14
  • \$\begingroup\$ If I understand correctly, your second code could be changed very slightly to become an answer to this challenge. \$\endgroup\$ – nedla2004 Nov 22 '16 at 2:08
3
\$\begingroup\$

C#, 337 bytes

There's a bit of rules abuse here. There's no restriction on leading space. Unfortunately, the canvas is finite, so there is an upper limit for n.

Indented for clarity:

using C=System.Console;
class P{
    static void Main(string[]a){
        int n=int.Parse(a[0]),d=2,x=250,y=500;
        var f="0D";
        while(n-->0)
            f=f.Replace("D","d3t03").Replace("T","10d1t").ToUpper();
        C.SetBufferSize(999,999);
        foreach(var c in f){
            n=c&7;
            d=(d+n)%4;
            if(n<1){
                var b=d%2<1;
                x+=n=b?1-d:0;
                y+=b?0:2-d;
                C.SetCursorPosition(x*2-n,y+d/3);
                C.Write(b?'_':'|');
            }
        }
    }
}
\$\endgroup\$
1
\$\begingroup\$

JavaScript (ES6), 220

Using the wikipedia formula for left and right turns.

n=>(d=>{for(i=x=y=d;i<1<<n;d+=++i/(i&-i))z=d&2,(w=d&1)?y+=z/2:x+=1-z,g=x<0?g.map(r=>[,,...r],x=1):g,g=y<0?[y=0,...g]:g,r=g[y]=g[y]||[],r[x]='_|'[w],w?y-=!z:x+=1-z})(0,g=[])||g.map(r=>[...r].map(c=>c||' ').join``).join`
`

Less golfed

n=>{
  g=[];
  for(i=x=y=d=0;i<1<<n;d+=++i/(i&-i))
    z=d&2,
    (w=d&1)?y+=z/2:x+=1-z,
    g=x<0?g.map(r=>[,,...r],x=1):g,
    g=y<0?[y=0,...g]:g,
    r=g[y]=g[y]||[],
    r[x]='_|'[w],
    w?y-=!z:x+=1-z
  return g.map(r=>[...r].map(c=>c||' ').join``).join`\n`
}

F=
n=>(d=>{for(i=x=y=d;i<1<<n;d+=++i/(i&-i))z=d&2,(w=d&1)?y+=z/2:x+=1-z,g=x<0?g.map(r=>[,,...r],x=1):g,g=y<0?[y=0,...g]:g,r=g[y]=g[y]||[],r[x]='_|'[w],w?y-=!z:x+=1-z})(0,g=[])||g.map(r=>[...r].map(c=>c||' ').join``).join`
`

function update() {
  var n=+I.value
  O.textContent=F(n)
}

update()
pre { font-size: 8px }
<input id=I value=5 type=number oninput='update()'><pre id=O></pre>

\$\endgroup\$
1
\$\begingroup\$

APL (Dyalog Unicode), 65 64 bytesSBCS

('_|'⍴⍨≢a)@a⍴∘''⊃1+⌈/a←(⊢-⌊/)⌈2+/÷∘¯2 1¨11 9∘○¨+\0,(⊢,0j1×⌽)⍣⎕,1

Try it online!

(⊢,0j1×⌽)⍣⎕,1 generates a list of steps as complex numbers. It starts from 1 and repeatedly appends (,) a reversed () copy of the list multiplied by 0j1=sqrt(-1).

+\0, prepend 0 and compute prefix sums

11 9∘○¨ decompose complex into (real;imaginary) pairs

÷∘¯2 1¨ divide the real parts by -2

2+/ sums of adjacent pairs

ceiling

(⊢-⌊/) subtract the minima from all, so that coords are non-negative

a← assign to a

⍴∘''⊃1+⌈/ create an empty char matrix such that the max coords can fit

('_|'⍴⍨≢a)@a put alternating _ and | at the coordinates from a

\$\endgroup\$

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