Logistic growth has three consecutive phases:
1) Somewhat chaotic start
2) Exponential growth (early adoption)
3) Logarithmic growth (late adoption)
If we look at the linear chart on the right, we see the characteristic exponential growth curve. It is what is known as a convex function ("it curves down bro"). In comparison, a logarithmic curve is a concave function ('curves up'). Here is a direct comparison, blue is exponential / red is logarithmic http://www.sosmath.com/algebra/logs/log4...
Obviously Bitcoin does not look logarithmic at this scale.
Log vs. Linear Charts
It is difficult to see the detail in the linear chart due to the large price difference over the years, so we need to switch to logarithmic to get a clearer picture of microtrends. The logarithm is simply as mathematical function not magic. Log charts are not more or less valid than linear charts, but we need to be aware of the distortions that occur during this transformation.
In trading we use a semilog chart. That means only one axis (price axis) is transformed logarithmically, the other axis (time) remains linear. This has the following effects on exponential and logarithmic curves:
1) Exponentials become linear, i.e. the become straight lines
2) The form of logarithms remains unchanged
Looking at the left chart, we see the underlying exponential form on the right has been transformed into a linear channel. Here is also another example: the same curve shown in log (left) and lin (right) charts
What's the Point?
To me it is clear that the is nothing in BTC history that shows we are undergoing logarithmic growth. The linear charts shows a perfect exponential and the log chart shows a clear linear channel. It represents stable exponential growth. Until the bottom of the channel is broken I do not consider those log charts that show logarithmic curves to be correct - just look at the linear chart!
The formations above the channel are the bubbles that grab the headlines. The stuff at the beginning, under the channel, represents the chaotic start of logistic growth. The bubbles are simply a runaway process that occurs when a certain set of conditions arise upon reaching the top of the exponential channel. If the price is not rejected, the channel top will be broken and a bubble may form. However the underlying exponential trend remains and a return to the mean is a return to this trend. That does not necessarily mean return to the bottom of the channel on the log chart straight away. The mean is actually the median of this channel. But the bottom of the channel is the fundamental support, so should be tested again at some point. This may occur sometime after bottoming.
Run some python to fit a proper exponential curve and determine the exponent for price long-term forecasts.
where a=4.24e-3 and b=0.94
This is same for second phase of logistic growth, f(x) = 2^x