Morse Code Tree

How to use

1. 1

   Press Dot or Dash, or the . and - keys, to walk down from Start. You can also tap any character in the tree.

2. 2

   Read the panel: the character, its code, how it sounds, its path from Start and the two branches below it.

3. 3

   To find a character or word, type it in Find. The tree jumps to it, and Play word lights each letter as it sounds.

4. 4

   Switch Mode to Hear and find. Press Play a character, walk to what you heard, then press Check.

5. 5

   Pick the characters and layout you want, then Download PNG or SVG, Print, or Print blank for a tree to fill in with its answer key.

What it does

An interactive Morse code tree of International Morse, from the site’s own code table, that you can walk, search, hear and print.

• Four setsLetters (the Morse code alphabet tree, 26), + Numbers (36), + Punctuation (54: every character and signal of ITU-R M.1677-1 up to six elements) and + Extensions (69, with common non-ITU symbols and accented letters, marked).
• Walk and readEach step shows the character, its code, how it sounds (dah-di-dah), its path and the next branches, with a link to the character’s own page.
• SoundEach step plays the code. Speed, tone and volume are the trainers’ shared sound settings.
• FindType a letter, number, symbol or word, up to 40 characters, to see each path. Prosigns go in angle brackets, like <SK>.
• Hear and findThe listen-and-trace exercise scouts do with a printed chart, with a score. Hide the letters to make it harder.
• Print and saveThe Morse code tree chart as PNG or SVG, or printed. Print blank gives a tree to fill in, then the answer key. Top down, or Sideways to fit a phone.

How it works

The rule

Start at the top. Each element of a code moves you one level down: a dot to the left branch, a dash to the right. A code with n elements sits on level n, and level n has room for 2ⁿ codes: 2, 4, 8, 16, 32, 64. The 26 letters fill the first four levels, 30 slots, and leave four empty in International Morse: ..--, .-.-, ---. and ----, which national tables use for Ü, Ä, Ö and CH. The digits sit on level 5 and most punctuation on level 6. Every code is from ITU-R M.1677-1, the standard for International Morse.

A binary tree with a catch

Each node has at most two children, one for a dot and one for a dash, so the Morse code binary tree is a true binary tree. But in a Huffman tree every letter sits on a leaf, and in Morse most letters sit on branches: E (.) is the start of A (.-), and A of W (.--). Morse is not a prefix code, so the receiver needs a gap to know a letter has ended.

The gap is the third symbol

Morse is sent with two states, on and off, but it uses three gaps. One unit separates the elements of a letter. Three units end the letter: on the tree, write down where you are and go back to Start. Seven units end a word. So -.- with short gaps is K, while the same elements with letter gaps are T E T. The timing follows ITU-R M.1677-1: a dash is three dots long.

Why E and T are at the top

The shortest codes went to the commonest letters. Alfred Vail estimated English letter frequency by counting the type in the type cases of a newspaper in Morristown, New Jersey (Wikipedia, Morse code). E and T got one element each and sit on level 1; rarer letters such as Q, Y and J sit on level 4.

The tree in code

Stored as an array, the tree needs no pointers: node i has its dot child at 2i and its dash child at 2i + 1, so walking a code is one line of arithmetic, and the bits of a letter’s position are its code. This Python decodes and encodes the 26 letters; extend the string to 64 or 128 characters for the numbers and punctuation.

# Levels 1 to 4 of the tree as one string: node i has its dot
# child at 2*i and its dash child at 2*i + 1; "*" is an empty slot.
TREE = "**ETIANMSURWDKGOHVF*L*PJBXCYZQ**"

def decode(code):
    i = 1  # Start
    for element in code:
        i = 2 * i + (element == "-")
    return TREE[i]

def encode(letter):
    i = TREE.index(letter)
    return bin(i)[3:].replace("0", ".").replace("1", "-")

print(decode("-.-"), encode("P"))  # K .--.

Examples

Every level of the tree with the + Punctuation set (every ITU character and signal up to six elements):

Check two walks by hand:

• K, −·−: the dash takes you right to T, the dot left to N, the dash right to K.
• 5, ·····: five dots, always left, through E, I, S and H. It is the bottom-left corner of the numbers; 0 (−−−−−) is the bottom right.