You have taken [00, 01, 10, 11], made a copy, reversed the copy, prepended each entry of the first list with 0, and prepended each entry of the copy with 1, and finally concatenated the two lists. But [00, 01, 10, 11] is not the correct starting point, [00, 01, 11, 10] is. This list is obtained by taking [0, 1], making a copy, reversing the copy, prepending each entry of [0, 1] and prepending each entry of [1, 0] with 1 and concatenating the two lists.

it changes one bit at a time in that way.

Shouldn't T(3) = [000, 001, 010, 011, 111, 110, 101, 100] instead of T(3) = [000, 001, 011, 010, 110, 111, 101, 100] ? Usually you write out bits in increasing order. Can some one explain to me in what order bits are written out in this kata ?