This is a Turing Machine that lists L_B in canonical order. Where L_B is the set formed by all natural numbers whose representation in binary is a palindrome.

TM-binary_palindrome_enumerator.yaml

name: binary palindrome enumerator
source code: |
  # Adds 1 to a binary number.
  input: ''
  blank: ' '
  start state: setup_a
  table:
    # binary generator
    setup_a:
      ' '     : {write: '#', L: setup_b}
    setup_b:
      ' '     : {write: 0, R: setup_b}
      '#'     : {L: check}
    right:
      [1,0]   : R
      '#'     : {L: add1}
    add1:
      1       : {write: 0, L}
      [0,' '] : {write: 1, L: left}
    left:
      [0, 1]  : L
      ' '     : {R: check}
    # Palindromo checker
    check:
      0       : {write: 'x', R: find_0}
      1       : {write: 'y', R: find_1}
      [x,y]   : {L: copy_back}
    find_0:
      [0, 1]    : R
      ['#', x, y]: {L: found_0}
    find_1:
      [0, 1]  : R
      ['#', x, y]: {L: found_1}
    found_0:
      0       : {write: 'x', L: next}
      1       : {L: no_copy_back}
      'x'     : {L: copy_back}
    found_1:
      1       : {write: 'y', L: next}
      0       : {L: no_copy_back}
      'y'     : {L: copy_back}
    next:
      [0, 1]  : L
      [x, y]  : {R: check}
    # Enumerator
    copy:
      x       : {write: 0, R: copy_0}
      y       : {write: 1, R: copy_1}
      '#'     : {L: end_word}
      [0, 1]  : R
    copy_0:
      [x, y, 0, 1, '#', '|']: R
      ' '     : {write: 0, L: copy_back}
    copy_1:
      [x, y, 0, 1, '#', '|']: R
      ' '     : {write: 1, L: copy_back}  
    copy_back:
      [x, y, 0, 1, '#', '|']: L
      ' '     : {R: copy}
    end_word:
      [x, y, 0, 1, '|', '#']: R
      ' '     : {write: '|', L: continue}
    
    no_copy:
      x       : {write: 0, R: no_copy}
      y       : {write: 1, R: no_copy}
      [0, 1]  : R
      '#'     : {L: continue}
    no_copy_back:
      [x, y, 0, 1]: L
      ' '     : {R: no_copy}
    # next binary number
    continue:
      [0, 1, '|']: L
      ' '     : {R: right}
      '#'     : {L: right}
positions:
  setup_a: {x: 40.25, y: 144.67}
  setup_b: {x: 121.72, y: 76.12}
  right: {x: 726.44, y: 322.03}
  add1: {x: 729.83, y: 195.09}
  left: {x: 731.96, y: 78.32}
  check: {x: 340.13, y: 32.22}
  find_0: {x: 445.03, y: 120.15}
  find_1: {x: 216.49, y: 114.7}
  found_0: {x: 512.01, y: 189.19}
  found_1: {x: 101.79, y: 191.7}
  next: {x: 346.72, y: 186.65}
  copy: {x: 318.38, y: 452.3}
  copy_0: {x: 99.08, y: 455.62}
  copy_1: {x: 324.66, y: 340.32}
  copy_back: {x: 101.93, y: 340.91}
  end_word: {x: 490.01, y: 451.19}
  no_copy: {x: 607.59, y: 381.76}
  no_copy_back: {x: 506.58, y: 331.39}
  continue: {x: 725.53, y: 452.15}

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