Introduction
The Baker's map is an important dynamical system that exhibits chaotic behavior. It is a function from the unit square to itself defined intuitively as follows.
- Cut the square vertically in half, resulting in two rectangles of size
0.5×1. - Stack the right half on top of the left, resulting in one rectangle of size
0.5×2 - Compress the rectangle back into a
1×1square.
In this challenge, you'll implement a discrete version of this transformation.
Input and Output
Your input is a 2D array of printable ASCII characters and whitespace of size 2m×2n for some m, n > 0.
Your output is a similar array obtained as follows, using the 6×4 array
ABCDEF
GHIJKL
MNOPQR
STUVWX
as an example. First, stack the right half of the array on top of the left half:
DEF
JKL
PQR
VWX
ABC
GHI
MNO
STU
Then, split the columns into pairs of characters, and independently turn each pair 90 degrees clockwise, "compressing" the tall rectangle back to the original shape:
JDKELF
VPWQXR
GAHBIC
SMTNUO
This is the correct output for the above array.
Rules
The input and output formats are flexible. You can use newline-delimited strings, lists of strings, or 2D arrays of characters. However, the input and output must have the exact same format: you must be able to iterate your submission an arbitrary number of times on any valid input.
You can write either a full program or a function. The lowest byte count wins, and standard loopholes are disallowed.
Test Cases
Input:
12
34
Output:
42
31
Input:
Hell
! o
d -
lroW
Output:
lol
o W-
!H e
ldr
Input:
ABCDEF
GHIJKL
MNOPQR
STUVWX
Output:
JDKELF
VPWQXR
GAHBIC
SMTNUO
Input:
*___ ___ o
o|__) |__) *
*| | o
o __ __ *
*| | _ o
o|__ |__| *
Output:
|_____) *o
|_ _ *o
||_ __| *o
o*|_____)
o* |_ _
o*||_ _
