Collatz Conjecture / Collatz Tree

[Arrow_Raider]

I have made a WPF application that constructs a Collatz Tree for the collatz conjecture problem. The collatz conjecture is that any number will eventually reach and terminate at 1 by following these steps:
If the number is even, divide the number by 2.
If the number is odd, multiply the number by 3 and add 1.
Repeat until number has reached 1.

Here is an example starting with 3:
3
10 (3x3+1)
5 (10/2)
16 (5x3+1)
8 (16/2)
4 (8/2)
2 (4/2)
1 (2/1)

The sequence starting with any number eventually reaches a 2^n number which is where it then begins to terminate.


My program (optionally) starts with 1 and shows the paths to reach 1.
Here is a screenshot:



The red numbers are numbers that satisfy the following: (n - 1) mod 3 = 2. All numbers under a red number will not branch out both directions; each of the red nodes can only have 1 child.

[Kasracer]

Neat. Never heard of that stuff but a none-the-less

[mendhak]

Nice. I've heard of Collatz before but it's obviously not as interesting as Happy Numbers. However, now that you've made a graph, you have upped the appeal of Collatz, giving Happy Numbers some real competition. Well done.

[wossname]

The graph is upside down and I don't like the colour.

[szlamany]

7 was coming after 11 - wasn't it...

It all makes sense now.

[szlamany]

9 and 14 as well - that's a curious spot - can you show the tree below that branch?

[Arrow_Raider]

I'll be releasing the source code soon, but I need to clean it up first.

Here is the tree under node 11:



This is the code I am using to generate the tree:

private BinaryTreeOfLong GenerateTree(int node, int n)
{
	if (n > 0)
	{
		BinaryTreeOfLong t = new BinaryTreeOfLong();
		t.Value = node;
		if ((node - 1) % 3 == 0)
		{
			if (((node - 1) / 3) % 2 == 1 && (node - 1) / 3 != 1)
			{
				t.LeftSubtree = GenerateTree((node - 1) / 3, n - 1);
			}
		}
		else if ((node - 1) % 3 == 2)
			t.Flag1 = true;
		t.RightSubtree = GenerateTree(node * 2, n - 1);
		return t;
	}
	else
		return null;
}

Note: BinaryTreeOfLong is basically BinaryTree<long>. I don't know how to get xaml to work with generics, so I just did it like that. I'll figure out how to use generics in xaml eventually... but I was too lazy yesterday.

[szlamany]

The "master numbers" behind 11 are remarkable...

But that's a different discussion.

[Arrow_Raider]

Do master numbers rule over mendhak's happy numbers?

[MaximilianMayrhofer]

Never.

[suryakantan]

Hi Arrow:

Can you post the entire code for the Collatz Tree?

Thanks.