Happy Fibonacci Day!

Question

Background

Today (or Yesterday) is (or was) 11/23 or Fibonacci day! What better way to celebrate than to make a Fibonacci cake?

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Examples

3

    ii
i_i_ii_i_i 

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8

              ii              
              ii              
              ii              
              ii              
              ii              
              ii              
              ii              
              ii              
            i ii i            
            i ii i            
            i ii i            
            i ii i            
            i ii i            
          i i ii i i          
          i i ii i i          
          i i ii i i          
        i i i ii i i i        
        i i i ii i i i        
      i i i i ii i i i i      
    i i i i i ii i i i i i    
i_i_i_i_i_i_i_ii_i_i_i_i_i_i_i

Challenge

^{You're not really making a cake, just the candles because I can't ascii-art a cake}

To make the cake you must first get the first n Fibonacci numbers sorted ascending. The candle (i)'s height is determined by value of the current Fibonacci number. The candles are separated by an underscore (_).

The cake should be symmetrical. So the candles should then be flipped and concatenated.

Example Construction

Input: 6
First 6 Fibonacci Numbers: 1, 1, 2, 3, 5, 8
Candle heights:

          i
          i
          i
        i i
        i i
      i i i
    i i i i
i i i i i i
-----------
1 1 2 3 5 8

Output would be:
          ii
          ii
          ii
        i ii i
        i ii i
      i i ii i i
    i i i ii i i i
i_i_i_i_i_ii_i_i_i_i_i 

Reference Fibonacci Numbers

For reference, here are the first 15 Fibonacci numbers. In this challenge, you'll be starting at 1.

1,1,2,3,5,8,13,21,34,55,89,144,233,377,610

Answer 1

J, 58 bytes

3 :''' i_''{~|.|:(,|.)(#&1,2#~0&=)"*}.,0,.(%-.-*:)t.1+i.y'

Uses (%-.-*:)t. for Fibonacci generation. Explanation might come a bit later.

Usage:

   f=.3 :''' i_''{~|.|:(,|.)(#&1,2#~0&=)"*}.,0,.(%-.-*:)t.1+i.y'
   f 5
        ii        
        ii        
      i ii i      
    i i ii i i    
i_i_i_i_ii_i_i_i_i

Try it online here.

Answer 2

CJam, 41 39 bytes

"i""_"1$ri({1$1$4$+}*]),f{Se[}W<_W%+zN*

This prints a fair amount of leading whitespace. Try it online in the CJam interpreter.

How it works

"i""_"1$ e# Push "i", "_", and a copy of "i".
ri(      e# Read an integer from STDIN and subtract 1.
{        e# Do that many times:
  1$     e#   Copy the last underscore.
  1$4$+  e#   Copy the last strings of i's and concatenate them.
}*       e#
]),      e# Wrap the results in an array, pop the last string, and get its length.
f{       e# For each remaining string, push the string and the length; then:
  Se[    e#   Pad the string to that length by prepending spaces.
}
W<       e# Remove the last string (underscore).
         e# We have now generated the columns of the left half of the output.
_W%+     e# Append a reversed copy (columns of right half).
z        e# Transpose rows with columns.
N*       e# Separate the rows by linefeeds.

Answer 3

TeaScript, 93 84 76 + 1 = 77 bytes

+1 byte for "Inputs are numbers?" checkbox

r×ß(p.R((w=F(x©-F(i¬©+"i"R(F(i¬±)t¡ß(j=i<w-1?" ":"_",(A=l¿i>0?j+l:l)µ)+Av©j§

Ungolfed version:

r(x)m(#(p.R((w=F(x))-F(i+1))+"i"R(F(i+1))))t()m(#(j=i<w-1?" ":"_",(A=ls``.m(#i>0?j+l:l)j``)+Av))j`
`

Thanks to @Vɪʜᴀɴ for the tips.

Answer 4

Python 2, 117 bytes

a=b='i'
l=a,
exec"l+='_',b,;a,b=b,b+a;"*~-input()
for r in map(None,*l+l[::-1])[::-1]:print''.join(x or' 'for x in r)

The idea is simple: generate the picture in columns going bottom to top, left to right, with the mirrored right half the reverse of the left. The columns are generated by iterating the Fibonacci recurrence, on strings of i's, interspersed with _'s for the bottom row.

To print the picture with columns starting from the bottom, we need to rotate it, which means transposing and reversing. Unfortunately, Python doesn't have a simple way to transpose an array of unequal-length rows. The built-in zip truncates to the shortest row. This uses the map(None,_) trick, but has to convert all the None to spaces afterwards.

Answer 5

Pyth, 31 bytes

jaPJ_.ts_BuaaGks>4GtQ]\idXeJ" _

Try it online: Demonstration

Explanation:

jaPJ_.ts_BuaaGks>4GtQ]\idXeJ" _   implicit: Q = input number
          u        tQ]\i          reduce the list [1, ..., Q-2], start with G=["i"]
            aGk                      append the empty string to G
           a   s>4G                  append the sum of the last 4 strings in G to G
                                  this gives ["i", "", "i", "", "ii", "", "iii",..]
       s_B                        extend the list with the reversed list
     .t                  d        pad to a rectangle with spaces and transposes
   J_                             reverse the order and assign to J
  PJ                              remove the last string of J
 a                                and append
                         XeJ" _   the last string of J with spaces replaced by "_"
j                                 print each string on a separate line

Answer 6

Haskell, 182 176 bytes

import Data.List
f=0:scanl(+)1f
b n c s|length s<n=b n c(c:s)|0<1=s
m s=s++reverse s
c n=mapM_ putStrLn$transpose$m$map(b(f!!n)' ')$intersperse"_"$map(\x->[1..f!!x]>>"i")[1..n]

Call c.

(f shamelessly stolen from https://stackoverflow.com/questions/232861/fibonacci-code-golf)

Answer 7

Jelly, 23 bytes

RÆḞ”iẋz⁶Ḣj”_ƊṭK€Ṛ$Ɗm€0Y

Try it online!

Jelly's not great at ascii-art and neither am I

How it works

RÆḞ”iẋz⁶Ḣj”_ƊṭK€Ṛ$Ɗm€0Y - Main link. Takes N on the left
R                       - [1, 2, ..., N]
 ÆḞ                     - k'th Fibonacci for each k in the range
   ”i                   - "i"
     ẋ                  - Repeat "i" k times for each k
      z⁶                - Transpose filling with spaces
                  Ɗ     - To this matrix:
            Ɗ           -   First:
        Ḣ               -     Pop and yield the first element (the base)
         j”_            -     Join with "_"
                 $      -   Then:
              K€        -     Join the other rows on spaces
                Ṛ       -     Reverse
             ṭ          -   Take the base onto the end of the rows
                   m€0  - Mirror each row
                      Y - Join on newlines

Answer 8

Matlab, 172 152 bytes

Unfortunately, Matlab hasn't a build in Fibonacci function and string Manipulation is a bit fiddly.

function t(n);f=@(n)getfield([0 1;1 1]^n,{3});m=char(flipud(bsxfun(@(a,b)(a<=f(b/2)&mod(b,2)==0)*'i',(1:f(n))',2:2*n)));m(end,2:2:end)='_';[m fliplr(m)]

With line breaks:

function t(n);
f=@(n)getfield([0 1;1 1]^n,{3});
m=char(flipud(bsxfun(@(a,b)(a<=f(b/2)&mod(b,2)==0)*'i',(1:f(n))',2:2*n)));
m(end,2:2:end)='_';
[m fliplr(m)]

Answer 9

Ruby, 151 146 142 137 132 bytes

->n{s=1,1;3.upto(n){s<<s[-1]+s[-2]};s.map!{|i|[' ']*(s[-1]-i)+[?i]*i}.transpose.map!{|a|v=a*'_ '[a.count(?i)<=>n];puts v+v.reverse}}

137 bytes

->n{s=1,1;3.upto(n){s<<s[-1]+s[-2]};o=s.map{|i|[' ']*(s[-1]-i)+[?i]*i}.transpose.map{|a|v=a*' ';v+v.reverse};o[-1]=o[-1].tr' ',?_;puts o}

142 bytes

->n{s=1,1;(3..n).map{s<<s[-1]+s[-2]};puts s.map{|i|[' ']*(s[-1]-i)+[?i]*i}.transpose.map{|a|v=a*' ';v+v.reverse}.tap{|c|c[-1]=c[-1].tr' ',?_}}

146 bytes

->n{s=1,1;(3..n).map{s<<s[-1]+s[-2]};puts s.map{|i|[' ']*(s[-1]-i)+[?i]*i}.transpose.map{|a|v=a.join' ';v+v.reverse}.tap{|c|c[-1]=c[-1].tr' ',?_}}

151 bytes

->n{s=1,1;(3..n).map{s<<s[-1]+s[-2]};puts s.map{|i|[' ']*(s[-1]-i)+['i']*i}.transpose.map{|a|v=a.join ' ';v+v.reverse}.tap{|c|c[-1]=c[-1].tr ' ', '_'}}

Ungolfed:

-> n {
  s = 1,1
  3.upto(n) {
    s << s[-1] + s[-2]
  }
  s.map! { |i|
    [' '] * (s[-1]-i) + [?i] * i
  }.
  transpose.
  map! { |a|
    v = a * '_ '[a.count(?i)<=>n]
    puts v + v.reverse
  }
}

Usage:

->n{s=1,1;3.upto(n){s<<s[-1]+s[-2]};s.map!{|i|[' ']*(s[-1]-i)+[?i]*i}.transpose.map!{|a|v=a*'_ '[a.count(?i)<=>n];puts v+v.reverse}}[8]

Output:

              ii              
              ii              
              ii              
              ii              
              ii              
              ii              
              ii              
              ii              
            i ii i            
            i ii i            
            i ii i            
            i ii i            
            i ii i            
          i i ii i i          
          i i ii i i          
          i i ii i i          
        i i i ii i i i        
        i i i ii i i i        
      i i i i ii i i i i      
    i i i i i ii i i i i i    
i_i_i_i_i_i_i_ii_i_i_i_i_i_i_i

Answer 10

Python 2, 213

Saved 12 bytes thanks to DSM.

def f(r):
 a=b=1
 while r:yield a;a,b=b,a+b;r-=1
n=list(f(input()))
n.remove(1)
h=max(n)-1
r=1
while h:
 l='  '*(len(n)+1)+('i '*r)[:-1];print(l+l[::-1]);h-=1
 if h in n:r+=1;n.pop()
l='i_'*r+'i_i'
print l+l[::-1]

Ungolfed version.

max_height = input()
def fib(r):
    a=b=1
    while r:
        yield a
        a,b = b, a + b
        r-=1

numbers = [x for x in fib(max_height) if x>1]
highest = max(numbers) -1
rows = 1
while highest:
    line =' '*((len(numbers)+1)*2) + ' '.join('i'*rows)
    print(line + line[::-1])
    highest -= 1
    if highest in numbers:
        rows += 1
        numbers.pop()

line = '_'.join('i'*(rows+2))
print(line + line[::-1])

Answer 11

Vyxal, 21 bytes

v∆F\i*∩vṄṘøɽvm‡\_ḞuV⁋

Try it Online!

How?

v∆F\i*∩vṄṘøɽvm‡\_ḞuV⁋
v∆F                   # For each item in [1, implicit input], get the nth fibonacci number
   \i*                # For each, repeat that many "i"s
      ∩               # Transpose
       vṄ             # Join each by spaces
         Ṙ            # Reverse
          øɽ          # Prepend leading spaces to each to right-align it
            vm        # Mirror each
              ‡\_ḞuV  # To the last item, replace spaces with "_"
                    ⁋ # Join on newlines