On the first bitcoin price chart below, the red and green parabolas are equivalent, with the green parabola shifted to the left 45 months.
The red parabola is defined by
D = 114.4 * ( 1.65 + log (usd price) )^2 Where D is days elapsed since Sept 8, 2010.
Map time onto time. As illustrated by the yellow line, 2014-07-01 maps to 887 days: the horizontal distance between that day's data point and the support line.
The transformation abstracts price data from the chart and makes the chart linear. Now we examine bitcoin’s cyclical behavior and model it.
The function shown in yellow below has a period of 1390 days, roughly bitcoin’s halving time.
Move back to the USD domain
and extrapolate.
Another view of the time transform:
