9846

Collatz Sequence Computed by a Turing Machine

The Collatz sequence is formed by an iteration of numbers produced by the following rule: If is even, then replace by ; if is odd then replace by . This Demonstration implements an 8-state 3-color Turing machine that computes this sequence.
The machine works like this: Write an initial number in base 2 on the blank tape. The head of the machine is initially located over the least significant byte of the number.
If is even, the head erases the digit 0 and moves to the left, so that it lies over the less significant byte of .
If is odd, the machine performs the sum by adding the number with itself shifted one position to the left plus one. To do this, the head writes 0, saves the digit 0 and the residue 1 and then moves to the left. Now, the head repeatedly adds the current digit plus the saved digit plus the residue saved in the head and saves the residue of the operation and the current digit in the head, then moves to the left. When the addition is done, the head returns to the position of the least significant byte of .
The computation does not stop at . It keeps computing the periodic sequence 1, 2, 4, 1, …, which can be interpreted as stopping.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+