TakenItSeriously

Adding Time to 2D PFHM

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I thought you guys might find this interesting.
 
Adding Time to a 2D Prime Factor Harmonic Matrix to demonstrate the “behavior” of standing vs moving prime factor “waves”
 
Previously I had introduced the Prime Factor Harmonic Matrix which showed that prime factors behaved like waves or specifically 1 dimensional waves that either behave like moving waves or standing harmonic waves within a 2 dimensional matrix of natural numbers.
 
A PFHM is simply any matrix of natural numbers that is dimensioned according to a primorial.
 
When this is done, the pattern of prime factors that make up the primorial behave like standing waves while prime factors that are not part of the primorial would behave like moving waves.
 
In order to better demonstrate this behavior, I added the dimension of time to a 2D 30x7 PFHM which is orthoganal to the plane.
 
Another words I created an animated gif which shows a progression of matrices level by level. i.e. 
210 = 2x3x5x7
  1. 1-210
  2. 211-420
  3. 421-630
  4. ...

ED066DCD-34B7-4AD4-88A9-8C13600065D5.gif.cabd4723019761ef51a945d005a41235.gif

Figure 1: A series of 30x7 matrices of natural numbers such that their prime factors are distributed periodically throughout the matrix. The slot on the left represents the factors of prime number 5, the second shows the factors of 7, the third shows the factors of 11 and the fourth shows the factors of 13. Each frame of the animation shows a progression of levels in the matrix.

Note that since 5 and 7 are both factors of the primorial 210, they never move or they behave like standing waves while all larger prime factor patterns each propagate at a different rate or a different “frequency over time”.

 

 

 
 
Edited by TakenItSeriously

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Just because it’s kind of cool to look at here is an expanded view of the animated 30x7 PFHM stack:

F2B354F6-D7D0-4C09-A653-BEF4127F352B.gif.12d57f892667402964b66c360d37c979.gif

Figure 2: An expanded view of the prime factor patterns.

Above is actually only a partial view of a large array of prime factor patterns in Excel. It starts in the upper left with the harmonic patterns for primes 2, 3, 5, & 7.

Each row actually contains 38 PFPs and the number of rows can extend indefinitely until Excel runs out of memory and crashes. Initially, I tried to include enough prime factors to define the primality up to the millionth matrix (numbers from 1 up to 210,000,000) which requires 1700 prime factor patterns for the primality to be fully defined. Oddly it was at the millionth matrix when Excel started crashing.

The animation represents matrix levels from 10,000 to 10,033 for 33 frames. I chose 33 frames so that the fifth prime (11) would appear to be smooth when displayed in a repeating loop.

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