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Challenges

Fibonascii Squares

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−0

The Challenge

Your job is to, given input positive non-zero integer $n$, output an ASCII representation of the tiled Fibonacci squares up to the $n$th number of the Fibonacci sequence.

Rules

Input:

  • Input will be an integer $n$ such that $n \gt 0$.

Output:

  • Output will be an ASCII representation of the tiled Fibonacci squares, up until the $n$th Fibonacci number.

  • For Fibonacci number $x$, its respective square will be $x$ characters tall and $x$ characters wide.

  • Squares must be tiled so as to match the arrangement shown in the examples below. However, the output may be mirrored or rotated by multiples of $90^\circ$ as desired. The orientation may be changed based on the input.

  • This challenge does include $0$ as a member of the Fibonacci sequence, so bear that in mind.

  • For cases where $n$ is $1$ (and hence there aren't any squares to create), you may either output any number of whitespace characters or output nothing at all.

  • Each square in the output must be represented by a grid made up of a unique ASCII character. For the characters forming your squares, you may use either the alphabet (either uppercase or lowercase, starting at a) or the digits 0-9 (starting at 0). You may reuse characters once you reach the end of the character sequence. You must use at least five unique characters.

  • This is a code-golf challenge, so the code with the fewest bytes wins!

Examples

Here is an image of the proper way to tile Fibonacci squares:

Fibonacci square arrangement.

Image source: Wikipedia

Example 1

Input:
6
Output:
DDDCC
DDDCC
DDDAB
EEEEE
EEEEE
EEEEE
EEEEE
EEEEE

Explanation: The input is $5$, representing the first $5$ numbers of the Fibonacci sequence, which are $0$, $1$, $1$, $2$, $3$, and $5$. The first and second squares are $1 \times 1$ characters in size, and are represented by A and B, respectively. The third square is $2 \times 2$ characters in size, and is represented by C, and so on until we reach the fifth square.

Example 2

Input:
1
Output:

Explanation: The input is $1$, representing the first number of the Fibonacci sequence, which is $0$. Thus, nothing is outputted. Alternatively, any number of whitespace characters could be outputted.

Example 3

Input:
3
Output:
AB

Explanation: The input is $3$, representing the first $3$ numbers of the Fibonacci sequence, which are $0$, $1$, and $1$. Thus, we have two squares, each $1 \times 1$ characters in size. The first square is represented by A, the second by B.

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2 comment threads

potentially wrong example (3 comments)
Varying rotation depending on input value (3 comments)

2 answers

+2
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BQN, 37 bytes

⍉∘⌽∘∾˜´(⍉{1⊸⌈⊸⋈⊑+`∘⌽⍟𝕩↕2}⥊'@'⊸+)¨∘⌽∘↕

-3 thanks to dzaima

The output isn't the same as the example but I think it's still correct if I understand the challenge correctly.

Result for x = 7:

FFFFFFFFEEEEE  
FFFFFFFFEEEEE  
FFFFFFFFEEEEE  
FFFFFFFFEEEEE  
FFFFFFFFEEEEE  
FFFFFFFFBADDD  
FFFFFFFFCCDDD  
FFFFFFFFCCDDD
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+2
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BQN, 29 28 bytes

(⍉≍""){⍉⌽𝕩∾˘𝕨⥊˜⋈˜≠𝕩}´⟜⌽'@'+↕

Try it here!

Explanation:

(⍉≍""){⍉⌽𝕩∾˘𝕨⥊˜⋈˜≠𝕩}´⟜⌽'@'+↕  # a function taking a single argument
 ⍉≍""                         # a 0-by-1 matrix
(⍉≍""){            }´         # right fold with the initial value of the 0-by-1 matrix
                     ⟜⌽       #   (but reverse the list to make it a left fold)
                           ↕  # range; 0 1 2 3 4 … input-1
                       '@'+   # plus the character '@'; "@ABCDEF…"

      {⍉⌽𝕩∾˘𝕨⥊˜⋈˜≠𝕩}          # fold operand: 𝕨 - current character, 𝕩 - accumulator - the matrix
                 ≠𝕩           # numbers of rows in the matrix
               ⋈˜             # paired with itself (7 → [7,7])
            𝕨⥊˜               # reshape 𝕨 that much
         𝕩∾˘                  # concatenate horizontally to 𝕩
       ⍉⌽                     # rotate 90° clockwise (reverse vertically, transpose)
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