Iterations with the fixed result: I want to make some curves from 0 to 1.

[GFabyz]

I want to make some curves from 0 to 1.
I need to calculate the growth variables of y from 0 to 1. So I tried this

int interations=1000;
float y, y_add=1./interations; // linear

for (int i; i<interations; i++) {
y += y_add; // linear
}

y result is 1 - works

float y_mlt = exp(-1/(interations)); // non linear slow grow on the first stage but fast grow in second
float a=0.582; // why it's 0.582 ?
y_add=a/interations;

for (int i; i<interations; i++) {
y = y*y_mlt + y_add; // non linear slow grow
}

y result is 1 - works

float y_mlt = exp(-1/(interations)); // non linear fast grow on the first stage but slow grow in second
y_add=(1+a)/interations;

for (int i; i<interations; i++) {
y = y*y_mlt + y_add; // non linear fast grow
}

y result is 1 - works



The calculation of a was made by more trying, in a primitive way.

What I want:
1. Where does the value of a come from?
2. How do I extend the calculation to get more curves with faster or slower growth?
3. Maybe find a variable of acceleration

 

[GFabyz]

interations it's variable, must work for any value

 

[GFabyz]

In the meantime I discovered some more things:

I managed to expand the formula and increase the acceleration as follows:

y_mlt = 1/exp(-q/interations); // slow grow on the first stage but fast grow in second
y_add=a/interations;

y_mlt = exp(-q/interations); // fast grow on the first stage but slow grow in second
y_add=(q+a)/interations;

I find a constants for q as integer number

q=1 - - - - - - a=0.582
q=2 - - - - - - a=0.313
q=3 - - - - - - a=0.1559
q=4 - - - - - - a=0.0743
q=5 - - - - - - a=0.0335

I don't know how to directly calculate these constants and extend the formula to decimal values for q

I suppose a series mean something, but what ?

 

[blamocur]

I want to make some curves from 0 to 1.
I need to calculate the growth variables of y from 0 to 1. So I tried this

This is very cryptic, and, I suspect, not many people will try figuring out your problem by reading your code. I suggest that instead you try defining your problem more clearly. This way you will increase your chances of getting meaningful help.

 

[GFabyz]

Have no idea how to explain. From my opinion is clear with example.

 

[blamocur]

Have no idea how to explain. From my opinion is clear with example.

It is far from clear to me. Here are some questions I have:

What does "...make some curves from 0 to 1" mean? Do you want to define a function analytically? Or tabulate it for a set of values between 0 and 1?

As for your examples, I don't see any curves there, only a computation of a scalar value [imath]y[/imath]. Do you mean that you are computing a sequence of [imath]y[/imath]'s and want to compute its "growth"? And do you need the average growth or growth at every point, i.e., every value of [imath]i[/imath] ?