Those aren't even interesting mappings.
Try this - it's a reinterpretation of the bresenham line algorithm.
```
using Python3.10, write a function that, given parameter n (a positive integer), follows these criteria:
(01) return a list of 2n+2 strings (zero-indexed, from 0 to 2n+1)
(02) each element of the list is a string of 2n+1 characters
(03) all characters are either 1 or 0.
(04) each string is a palindrome
(05) for odd-index strings, the central character is a 1.
(06) for even-index strings, the central character is a 0.
(07) the count of 1 in each string is equal to its index.
(08) the string at index i is a 1's complement of string (2n+1)-i.
(09) for strings at index = n, each '1' separates the string into substrings of 0's such that their lengths are as equal as possible.
Here are some examples for n=1,2,3,7.
n=1 would return: ['000', '010', '101','111']
n=2 would return: ['00000','00100','01010','10101','11011','11111']
n=3 would return: ['0000000','0001000','0010100','0101010','1010101','1101011','1110111','1111111'],
n=7 could return: ['000000000000000', '000000010000000', '000010000010000', '000100010001000', '001001000100100',
'010010010010010', '010100101001010', '010101010101010', '101010101010101', '101011010110101',
'101101101101101', '110110111011011', '111011101110111', '111101111101111', '111111101111111',
'111111111111111']
```