[PD] exponential tempo control

[Mathieu Bouchard]

On Sun, 30 Oct 2005, Chuckk Hubbard wrote:

> I should be writing math textbooks.
> What does anyone use this particular equality for?

it's used in the formula for computing logarithms and cartesian-to-polar.

given f(x) = sum of x^n for n from 0 upwards = 1/(1-x),

then its integral F(x) = sum of (x^n)/n for n from 0 upwards =
-log(1-x)

And combining complex numbers with log, you get atan, a function that 
turns slopes into angles.

Chances are that your CPU computes log and atan by applying such formulas.

There are many many other applications. Because it's a very simple 
formula, chances are many people encounter that pattern in many 
different situations. The place where I've used it most is in 
Probability Theory (!!!).

____________________________________________________________________
Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju
Freelance Digital Arts Engineer, Montréal QC Canada