Collatz code

Almost 2 years ago - I remembered about a puzzle my maths teacher gave us. It went something like this:

"Start with any positive number. If it's an even number, divide that number by two. If it's odd, multiply your number by three and add one. Then repeat with the number you have.

"Continue," he said. "And you will likely always return to one." 

I started with 72. Dividing that by 2, I got 36, then 18, then 9. I multiplied 9 by 3 to get 27, and added 1. 28 is even, so that becomes 14, then 7. 7 multiplied by 3 and add 1, is 22, which can be divided to 11. Then there was 34, 17, 52, 26, 13 before things seem to get there. 13 transforms to 40, which can be divided by 2 to give 20. Then 10. Then 5. 

At this point, I wondered where we were going next. 

Well, the next number was 16, a power of two. Then 8, 4, 2, 1. 

Ta dah!

After I'd remembered this fun, number game I wanted to learn more about it. A quick Google search yielded that it was called the Colatz conjecture and that it's unsolved. You may have spotted that my maths teacher said that you will "likely return to one", with any number you pick. He said "likely" because no one has proven if that is the case. 

I discovered that people have used computers to show that all numbers up to a ludicrously large number follow this pattern: but that is not enough to prove that the pattern must work for all numbers.

That got me thinking that maybe I could write a quick-and-dirty Python program (available on GitHub) to calculate the number of steps each value up to N takes to get to 1. So I did that. My code takes a .csv file containing a range of values which will go into the Colatz code as input. And it returns a .csv file with the same inputs next to a count of the number of steps it took to get to 1.

I could use this output to draw a pretty chart showing the number of steps each input value takes to get to 1. 

A pretty chart showing the number of steps each input number up to 1,000 (I wasn't very ambitious!) takes to return to 1.

I obviously haven't proved anything, other than to myself, that hobbyist coding is fun and creates nice patterns sometimes. 

I enjoy having these little project swimming around in my head, perhaps placed on the back burner for months. Recently I've started thinking about the Collatz conjecture again - and that I'd like to write more (efficient) Python code to find more patterns.

Comments

Post a Comment

Popular posts from this blog

level 17

Image
http://www.deathball.net/notpron/finale/pron.htm "aliens are coming" Source code says "what am i?" After the image file. 1. What are you looking at? 2. It's clear there is no link, so you don't need to look for a user name and password. 3. You ned to change the URL. 4. Keep guessing what you are looking at. 1. I tried "/ufo.htm" and got wrong way. 2. Then I tried "/egg.htm" and got another wrong way. 3. One of the "Wrong Way" clues says you have seen this before. 4. I guessed "/lamp.htm" which was RIGHT! :)
Read more

Level 16

Image
http://www.deathball.net/notpron/zoo/mznvh.htm This is the image you are presented with. It's clear upon first inspection that each of the squares corresponds to each of the previous 15 levels. 1. The source code says "invert a-z" 2.Could this have something to do with the URL? 3. What do the numbers in the pictures mean? 4. What does # mean? 5. Apply what you've been told to the levels referred to. 1. Inverting the letters in the URL gives. "all/names.htm" 2. You know it has to do with the usernames of the levels concerned. 3. The # indicates that the name is inverted (the clue is in the source code) 4. The numbers in the boxes must refer to the letter number of the user name for that level. 5. When there is a # after the number that means, invert the letter. 6. Combining all the letters from the usernames you get the following DOOM MURDER And there's the Username and Password :)
Read more

This is notpr0n...

OK! I've had a new idea for this blog. I'm supposed to be revising! HAH! So obviously I've started playing notpr0n again! It's a massive online click and play webriddle! And it's nigh on impossible (for me anyway) without help. So I've decided to go through each level I've down and write hints and teasers for each level, then in a black font I'll write the solution to each level. This was, those who don't want to see the answer don't have to. And those that do want to see the answer simple have to -A to select all writing on the page and view the solution. 1 last thing, I can't be bothered doing all the levels, so I'll start from where I left off before I started revising (in my opinion this is wher eit starts getting hard. LEVEL 16 FOLLOWS!
Read more