This equation is the core. This could be viewed as the differential flow (in one dimension) of anything. I would write this program as:

#include <stdio.h> int main(int argc , char * argv[]){ const int h_length=20; float HD=0.0; float H[h_length]; float k=2.0; int l=0; int i; for (i=1;i<h_length;i++) { H[i]=0.0; } H[0]=100.0; while (H[0] < 6.0) { l+=1; printf("%d %f %f \n",l,H[0],H[h_length-1]); for (i=1;i<h_length;i++) { HD=(H[i-1]-H[i])/k; H[i]+=HD; H[i-1]-=HD; } } return 0;}

What this works out to is a process that describes linear transfer. What happens in general is that as time passes, each term is divided over and over again until it reaches the end of this array. That is a simulated bar of metal of some length and with a specific heat transfer rate and some time interval that goes to 0. The difference between 0 and 1 is 1/n and the difference then in the next step is 1/n^2 and so on. This may well be the wrong equation to start with. My experience with momentum and interaction in systems leads me to choose a different approach to this. What this describes is a one dimensional boundary condition which is applicable to all momentum systems, which is everything in this universe I have seen.

It gets more complex from here and that just makes for more fun. I am beginning to see some new relationships here and this looks like a number that could have some important cousin numbers. There is good reason why e^{t} is very meaningful. 't' is the while. Very interesting stuff. If you change the equation a little it could even describe a vampire I know.

ADDED: After implementing this and graphing the result it was obvious that it was not exactly what I wanted and there is some interaction with the FPU limits of digits. Using double and excluding FPU sign on below threshold values it becomes this done in reverse order, which is more reasonable.

for (i=h_length;i>0;i--) { HD=(H[i-1]-H[i])/k; if( HD > 0.0){ H[i]+=HD; H[i-1]-=HD;} }

It is very interesting as the graphic is very fluid and natural, as you would expect from something that simulates a natural thing.

I have a 3 dimensional version of the Fourier-like infinite series and it is my assumption that I will have an n-dimensional universal transfer equation when I am done. The spatial conversions with relativity are quite convoluted and so I will test for a while and do some repairs so I can do some more videos and have the equations, code, videos, and animated gifs on the web page as links so they don't clutter the blog.

I managed to make a major breakthrough in the mathematics of angular motion which hopefully will help to simplify the perception and use of complex angular systems like gyroscopes.

By applying any recursive function I should get various types of wave motion. My opinion is that there are two types of sines or perhaps a combined sin(2Πx)*f(x) relationship which is perhaps what is considered the "imaginary" component. Oh well, I wonder how many people will be able or even care to follow this into a new way of looking at the root mathematical algorithms.

I am not sure whether I mentioned that I had included 2 and 3 dimensional function mapping and graphical capabilities into af. If I didn't mention it, well there it is now. This particular graph is scaled in Y by 0.20. While looking at that I decided I would add difference mapping in red on top of the elements.

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