It needs work, but it gets the shape of the currency's Price as a function of time P(t) as well as respectably reproducing the log plot. The model is very senesitive to the "effective bitcoin supply" in the denominator. Anyway, have at it I'd love to see some noise added, or other artifacts

(* 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}] *)