If even do this / if odd do that

The Collatz Conjecture is an unusual equation. So far, any # that has been entered into this equation [3X + 1 if odd] [ value / 2 if even] (up to 295,147,905,179,352,825,856 with is 2^68) eventually comes down to 1. No Loops have been found on the positive side. 3 Loops have been found on the negative side.

A seed of 6

3X + 1 >> Choose any seed number for X. Lets choose 5. If 5 is odd, then feed 5 into the formula 3X + 1. The results being 3*5+1 = 16. If the # for X was even, then divide the value by 2. So in this case, 16 / 2 = 8, 8 / 2 = 4, 4 / 2 = 1, 2 / 2 = 1. With a seed of 5, the number of formula steps is 6 when it approaches the value of 1.

Control Panel Variables

The seed variable (101) is where you want to start the dynamic graph at for the Collatz conjecture. As you can see in the second image below 101 is on the first green cube. Next in line is 304 so we arrive here by going 101 * 3 + 1 = 104. Since 304 is even we divide by 2 so that 304 / 2 = 152. Divide by 2 again 152 / 2 =76, 76 / 2 = 38, 38 / 2 = 19, since 19 is odd 3 * 19 + 1 = 58, 58 / 2 = 29, 29 is odd so 3 * 29 + 1 = 88, 88 / 2 = 44, 44 / 2 = 22, 22 / 2 = 11, 3 * 11 + 1 = 34, 34 / 2 = 17, 17 * 3 + 1 = 52, 52 / 2 = 26, 26 / 2 = 13, 13 * 3 + 1 = 40, 40 / 2 = 20, 20 / 2 = 10, 10 / 5 = 2, 5 * 3 + 1 = 16, 16 / 2 = 8, 8 / 2 = 4, 4 / 2 = 2, 2 / 2 = 1 and the bottom is reached for this sequence. With the seed starting at 101 there are 26 steps until #1 is reached. This was calculated from the Iterations equation using the DistanceToOneFunction in the CollatzConjecture class.

The MaxValue is a computed value for informational sake via a c# function in the Initialization.cs class under the Classes Project Node in MathCompiler3D.

The Spacing variable will control the horizontal spread of each of the dynamically graphed #'s.

When you first start to experiment with the Collatz Conjecture - start will small Seed values and get to know the extent of the functionality - then slowly raise the value as you study the progression.

DivideByScale: Controls the vertical expanse of the dynamic graph. This is Seed / 10.

DivideByScale: Controls the vertical expanse of the dynamic graph. This is Seed / 20.

Rotating Collatz Conjecture

Summation

Have fun researching 3X + 1. You should know that Math professors advise young mathematicians not to work on this problem because they will "waste their life." That being said, you might come up with the answer. See if you can improve upon the dynamic graphing and C# included in this project to study the Collatz Conjecture. When you alter this pattern by a small # of degrees shifted to the left or right, it has a very similar pattern to wheat - which might be a subtle indication that math is at the based of certain types of plant growth - what else in nature does it related to? You could be the one who figures it out!