drakoin ask
"the total number of addresses as a function of time ?"
here the answer:
Addresses = 2764582*exp((days from 01/01/2012)*0.00297)
that extimate for the end of 2014 about 71.000.000 of total addresses (active + zero)
Thanks a lot. Very nice. That predicts
16 billion addresses on the 1.1.2020 = 2 addresses per human
(if we make it that far without a collapse of the ecosphere).
Now I can do what I had wished for.
You cleverly related the number of addresses through a network effect to the price. So when everyone has a BTC address, the price will saturate, right? That would be around 2019 or 2020 if we adventurously extrapolated your fit that far.
With P(1.1.2020)~1.6*10^9 USD we now have
a first upper bound for the price t\to\infty :
It is unlikely that 1 bitcoin will ever cost more than 1 billion (of todays') USD.
Hmmm .... BTC is given in 0.00000001 units.
But no worries, that 1 billion USD per 1 BTC is an over-exaggeration - probably *g* The underlying model would be limitless exponential growth, anyways. Not gonna happen.
Your model is ~Exp(t) for these two years.
So what we might see right now is the exponential phase of a transformation.
If that happens like a
logistic function which is one of the S-shaped curves, the fast increase slows down long before half of the maximum.
In phase transition approximating simulations, however, we see that ... the larger the model, the steeper the slope in the middle (cannot find a picture now, it does look different but a bit
similiar to such curves) - fastest up to a critical point around which the acceleration changes sign, and afterwards the system slower and slower approaches it's maximum. It's difficult to predict the critical point in a phase transition before it actually happens.
OR the whole thing is just an exponentially growing ... bubble.
.
.
Next story, how to simplify your second result.
Like in #57, I am playing a bit with your formula.Addresses = 2764582*exp((days from 01/01/2012)*0.00297)
Your 2764582 actually represents almost exactly 5000 days :-)
exp(4994.07408 * 0.00297) = 2764582 ... within the precision of a fit ... that's 5000.
So it's "exp((5000 days plus the days since 01/01/2012)*0.00297)", which can be stated even easier...
My first reformulation
Addresses = exp ( (days since 30/4/1998) * 0.00297 )
gives the same results as yours, it's only off by 0.02%.
.
Your 0.00297 = 1/337 is almost the years per day. A year I took to be 365 days (ignoring the 365.249... for now :-) )
So my best version is
Addresses ~= exp ( years since 1/1/1997 )
which for today is accurate to 0.13% !!!
Of course, for the future, that predicts too few addresses, but still, even for 2019 it's only off by 50%.
And it's remarkably simple, don't you agree?
So here comes my contribution to the marketing of your research:
The number of bitcoin addresses can be fitted approximately like
exp(years since 1.1.1997) = " 2.71828 to the power of (years since 1.1.1997) " 
