Blog post: Unity+: Curvature Limits and the Lambda Function of Derivatives

In Calculus, limits are what approach a certain value of x without ever equaling the value of x. For example, the following would be a way limits work.

As seen in this limit, the value of x approaches infinity, which means that the solution to this problem is 0 because 1/? is equal to 0. This kind of concept would be what occurs with curvature limits, but in a different fashion. Before explaining curvature limits, here is an example of a curvature limit being applied to the Lambda Function of Derivatives.

In this case, the limit is merely an extension of the equation. It shows that the Lambda function is a curvature limit, where the function that is a result is the solution to the curvature limit. For a demonstration, here is an animation of what a curvature limit would look like.

The above animation is a result of the curvature limit of the Collatz parameters, with 1 being the reference frame and the value of n, or 27, being what is tested relative to 1.

Now, in the animation above, there were only Collatz numbers that were tested for iteration which means that Collatz numbers act as the compositions of this curvature limit. Here is the Hailstone sequence of 27 where the Collatz numbers are bolded.

{ 27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91,274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1 }

This means that Collatz numbers have an important role in curvature limits. It also means that the derivative of a function and its inverse has a strong relevance to the curvature limit. There are many hypotheses, or conclusion, that can be made from this type of phenomena.

There are many conclusions that can be made from this phenomena, but more research would have to be made in order to make a better conclusion. Again, thank you for reading.
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