An H tree is a fractal tree structure that starts with a line. In each iteration, T branches are added to all endpoints. In this challenge, you have to create an ASCII representation of every second H tree level.

The first level simply contains three hyphen-minus characters:

---

The next levels are constructed recursively:

• Create a 2x2 matrix of copies from the previous level, separated by three spaces or lines.


• Connect the centers of the copies with ASCII art lines in the form of an H. Use - for horizontal lines, | for vertical lines, and + whenever lines meet each other.

Second level

-+-   -+-

 |     |

 +-----+

 |     |

-+-   -+-

Third level

-+-   -+-   -+-   -+-

 |     |     |     |

 +--+--+     +--+--+

 |  |  |     |  |  |

-+- | -+-   -+- | -+-

    |           |

    +-----------+

    |           |

-+- | -+-   -+- | -+-

 |  |  |     |  |  |

 +--+--+     +--+--+

 |     |     |     |

-+-   -+-   -+-   -+-

Rules

• Input is an integer representing the level of the ASCII art H tree as described above (not the actual H tree level), either zero- or one-indexed.


• Output is flexible. For example, you can print the result or return a newline-separated string, a list of strings for each line, or a 2D array of characters.


• You must use -, |, + and space characters.


• Trailing space and up to three trailing white-space lines are allowed.

This is code golf. The shortest answer in bytes wins.

Canvas, 20 19 bytes

ø⁸«╵［↷Ｌ⇵；ｌ⇵└┌├-×╋‼│

Try it here!

Explanation:

ø                    push an empty canvas

 ⁸«╵[              repeat input*2 + 1 times

     ↷               rotate clockwise

      L⇵             ceil(width/2)

        ;l⇵          ceil(height/2); leaves stack as [ ⌈½w⌉, canvas, ⌈½h⌉ ]

           └┌        reorder stack to [ canvas, ⌈½w⌉, ⌈½h⌉, ⌈½w⌉ ]

             ├       add 2 to the top ⌈w÷2⌉

              -×     "-" * (2 + ⌈w÷2⌉)

                ╋    in the canvas, at (⌈w÷2⌉; ⌈h÷2⌉) insert the dashes

                 ‼   normalize the canvas (the 0th iteration inserts at (0; 0) breaking things)

                  │  and palindromize horizontally

Charcoal, 22 bytes

Ｐ-²ＦＮＦ²«⟲Ｔ²+×⁺²κＸ²ι←‖Ｏ

Try it online! Link is to verbose version of code. 0-indexed. Explanation:

Ｐ-²

Print the initial three -s, leaving the cursor in the middle.

ＦＮ

Repeat for the number of times given.

Ｆ²«

Repeat twice for each H. Each loop creates a slightly bigger H from the previous loop, but we only want alternate Hs.

⟲Ｔ²

Rotate the figure.

+×⁺²κＸ²ι←

Draw half of the next line.

‖Ｏ

Reflect to complete the step.

The result at each iteration is as follows:

---



|   |

+---+

|   |



-+-   -+-

 |     | 

 +-----+ 

 |     | 

-+-   -+-



|   |   |   |

+-+-+   +-+-+

| | |   | | |

  |       |  

  +-------+  

  |       |  

| | |   | | |

+-+-+   +-+-+

|   |   |   |



-+-   -+-   -+-   -+-

 |     |     |     | 

 +--+--+     +--+--+ 

 |  |  |     |  |  | 

-+- | -+-   -+- | -+-

    |           |    

    +-----------+    

    |           |    

-+- | -+-   -+- | -+-

 |  |  |     |  |  | 

 +--+--+     +--+--+ 

 |     |     |     | 

-+-   -+-   -+-   -+-

Python 2, 227 bytes

L=len

def f(n):

 if n==1:return[['-']*3]

 m=[l+[' ']*3+l for l in f(n-1)];w=L(m[0]);y=L(m)/2;x=w/4-1;m=map(list,m+[' '*w,' '*x+'-'*(w-x-x)+' '*x,' '*w]+m)

 for i in range(y,L(m)-y):m[i][x]=m[i][w+~x]='|+'[m[i][x]>' ']

 return m

Try it online!

Perl 6, 118 bytes

{map ->y{map {' |-+'.comb[:2[map {$^b%%1*$b&&6>=$^a/($b+&-$b)%8>=2},$^x/¾,y/2,y,$x/3-$_]]},2..^$_*6},2..^$_*4}o*R**2

Try it online!

0-indexed. Returns a 2D array of characters. The basic idea is that the expression

b = y & -y   // Isolate lowest one bit

b <= x % (4*b) <= 3*b

generates the pattern

--- --- --- ---

 -----   ----- 

--- --- --- ---

   ---------   

--- --- --- ---

 -----   ----- 

--- --- --- ---

Explanation

{ ... }o*R**2  # Feed $_=2**$n into block

map ->y{ ... },2..^$_*4  # Map y=2..2**n*4-1

map { ... },2..^$_*6      # Map $x=2..2**n*6-1

' |-+'.comb[:2[ ... ]]    # Choose char depending on base-2 number from two Bools

map { ... }  # Map coordinates to Bool

  # Horizontal lines

  ,$^x/¾  # Modulo 8*¾=6

  ,y/2    # Skip every second row

  # Vertical lines

  ,y      # Modulo 8

  ,$x/3   # Skip every third column

   -$_    # Empty middle column

# Map using expression

$^b%%1*$b&&  # Return 0 if $b is zero or has fractional part

6>=$^a/($b+&-$b)%8>=2  # Pattern with modulo 8