Ian Carpenter (@IanMathmogician on Twitter) came up with the following very cute dynamical process, based on whole numbers:

1. Pick a number between 1 and 99.

2. Write the number as words.

3. Count the number of letters in the words to get a new number.

4. Repeat.

What happens?

Suppose we start with 42.

We write this as “forty two”, which has 8 letters.

We now write 8 as “eight” which has 5 letters.

We write 5 as “five” which has 4 letters.

We write 4 as “four” which again has 4 letters, so we’re stuck on 4.

Turns  this always happens, no matter where you start.

 How about French?

What if we did the same process in French?

42 -> quarante deux ->12 -> douze -> 5 -> cinq -> 4 -> quatre -> 6 -> six -> 3 -> trois ->5

so we get a cycle in French: 5-> 4 -> 6 -> 3 -> 5

What if we start at another number?

How about your language?

What happens in your language?

Hungarian?

Vietnamese?

Try it, and let us know.

 Matt Henderson, @matthen2 on Twitter, who is a very clever fellow, has produced some lovely pictures of this dynamical process.

What happens if you choose numbers bigger than 99? Explore!

 Postscript

Jim Wilder, @wilderlab on Twitter, pointed to the Web page Mathemagical Black Holes by Dr. Mike Ecker which has this and two other similar dynamical processes for whole numbers.

Also see the references to Ecker’s processes given by Alex Bogomolny, @CutTheKnotMath on Twitter, here and here.