I figured out the probability function which represents demandwas a logistic curve closely related to Tanh[t]. Then it was all pretty smooth...the model absolutely NEEDS the supply of bitcoin to distinctly less than a linear function or else it doesn't go well but yeah, this model does seem to loosely respect the large time scale behavior we have seen of bitcoin.
Here is a google drive with the mathematica files as well as outputs as PDF's of the plots, the raw text files, and "CDF" files which apparently are computable even if you don't own mathematica but I'm not sure.
https://drive.google.com/folderview?id=0B2HU2oGcAN_SSllnYkd0VThTcW8&usp=sharingThis is the main idea of the code there though there is a bit more in the google drive... this will get a dynamic set of plots going you can mess with with your hands varying parameters. The plot shapes all look pretty good and are extremely sensitive to the supply function controlled by the parameter th:
(* Bitcoin price model plotter // Altoidnerd 2013*)
Demand[t_] := 1/(1 + Exp[-t/tp])
Supply[t_] := t*2^(-t/th)
{Slider[Dynamic[tp], {0, 29, .1}, ImageSize -> 1300],
Dynamic[tp], "= propogation time tp" ,
Slider[Dynamic[th], {0, 3, .00001}, ImageSize -> 1300],
Dynamic[th], "= effective bitcoin supply"}
Dynamic[
Plot[Demand[t]/Supply[t], {t, .0000001, 20}, ImageSize -> 500,
AspectRatio -> 1/1.6^2]]
Dynamic[
Plot[Log[Demand[t]/Supply[t]], {t, .0000001, 20}, ImageSize -> 500,
AspectRatio -> 1/1.6^2]]
(* You can comment out this table if you just want to use the sliders \
to mess with the graph. If you run both the dynamics and the table \
you'll see a cool animation but after that you'll be manipulating \
over 200 plots simultaneously*)
(* Table[
{Plot[Demand[t]/Supply[t],{t,.001,5},ImageSize\[Rule]500],
Plot[Log[Demand[t]/Supply[t]],{t,.01,5},ImageSize\[Rule]500]},{th,1*\
10^-3,.9995,5*10^-3}] *)