So what does this chart mean for bitcoin?

[mobodick]

I found this nice line to bitcoin price.
But it seems systematic and not related to what's going on on the exchanges.
It's almost like a built in system.
Can anyone offer an explanation for this mathematically simple rise of minimal price?

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[Comodore]

This is great. It gives confidence.

[Etlase2]

Can anyone offer an explanation for this phenomenon?

Somebody drew a line on a graph? One that is not linear and apparently not even logarithmic no less?

[mobodick]

Can anyone offer an explanation for this phenomenon?

Somebody drew a line on a graph? One that is not linear and apparently not even logarithmic no less?

Exactly!

To be more specific, i photoshopped in a plot of the form y=x^z

[Comodore]

Can anyone offer an explanation for this phenomenon?

Somebody drew a line on a graph? One that is not linear and apparently not even logarithmic no less?

Exactly!

To be more specific, i photoshopped in a plot of the form x=y^x

Hmm, You got me.

[pretendo]

I wonder if the maker of this chart drives his destinations by using the patterns of the roads behind him

[mobodick]

I wonder if the maker of this chart drives his destinations by using the patterns of the roads behind him

This is not a thread about driving, this is a thread about why the hell bitcoin value has such a mathematically simple bottom.

[notme]

Can anyone offer an explanation for this phenomenon?

Somebody drew a line on a graph? One that is not linear and apparently not even logarithmic no less?

Exactly!

To be more specific, i photoshopped in a plot of the form x=y^x

So y = the x'th root of x?

[ElectricMucus]

The explanation is you can derive some lower bond curve for every possible chart.

[mobodick]

Can anyone offer an explanation for this phenomenon?

Somebody drew a line on a graph? One that is not linear and apparently not even logarithmic no less?

Exactly!

To be more specific, i photoshopped in a plot of the form x=y^x

So y = the x'th root of x?

LOL, yes,
brainfart i guess.

It's y=x^z and z is someting like 0.55

[mobodick]

The explanation is you can derive some lower bond curve for every possible chart.

But could you then go on and describe this curve with one term?

[ElectricMucus]

The explanation is you can derive some lower bond curve for every possible chart.

But could you then go on and describe this curve with one term?

It's not one term. And yes you can do the exact same thing you did on every chart. Just plot Brownian motion on a chart and do it, you'll see.

[Spekulatius]

I think this chart can best be explained with the money people put into bitcoin by converting fiat or other assets to bitcoin.
Its getting more and more over time but at a decreasing rate, because to expand the market capitalization at the beginning was cheap, to expand it by the same degree right now takes considerably more money! As with all growth processes in reality, that are restricted by finite resources (like value supply), this growth rate will finally reach its maximum, or grow increasingly smaller as the consumed resources dwindle. I think what we see here is the result of just that. It will continue to grow till a certain saturation is achieved in which mediums of value converted into and out of bitcoins balance each other out. What the function symbolyses is the sum of all value traded for bitcoin. Price can outperform this level fueld by speculation and expectations but finds it hard to drop below for some reason. It may be because holders of bitcoin still remember the value they put into bitcoin to aquire them and therefore refuse to trade them in for less. This effect, if valid, would further strenghten this bottom line and push price up.

I guess that more then the two effects are at play here and work in conjunction with one another. What they are remains to be seen.

[mobodick]

The explanation is you can derive some lower bond curve for every possible chart.

But could you then go on and describe this curve with one term?

It's not one term. And yes you can do the exact same thing you did on every chart. Just plot Brownian motion on a chart and do it, you'll see.

But what i drew IS a one term function (made with a graph tool).
That's why i think it's special.

[Spekulatius]

The explanation is you can derive some lower bond curve for every possible chart.

But could you then go on and describe this curve with one term?

It's not one term. And yes you can do the exact same thing you did on every chart. Just plot Brownian motion on a chart and do it, you'll see.

No you cant. If price drops below the red line it wouldnt be valid anymore. It would rather show an average direction, which is what you can REALLY do with every chart.

[mobodick]

I think this chart can best be explained with the money people put into bitcoin by converting fiat or other assets to bitcoin.
Its getting more and more over time but at a decreasing rate, because to expand the market capitalization at the beginning was cheap, to expand it by the same degree right now takes considerably more money! As with all growth processes in reality, that are restricted by finite resources (like value supply), this growth rate will finally reach its maximum, or grow increasingly smaller as the consumed resources dwindle. I think what we see here is the result of just that. It will continue to grow till a certain saturation is achieved in which mediums of value converted into and out of bitcoins balance each other out. What the function symbolyses is the sum of all value traded for bitcoin. Price can outperform this level fueld by speculation and expectations but finds it hard to drop below for some reason. It may be because holders of bitcoin still remember the value they put into bitcoin to aquire them and therefore refuse to trade them in for less. This effect, if valid, would further strenghten this bottom line and push price up.

I guess that more then the two effects are at play here and work in conjunction with one another. What they are remains to be seen.

Interesting!

[ElectricMucus]

The explanation is you can derive some lower bond curve for every possible chart.

But could you then go on and describe this curve with one term?

It's not one term. And yes you can do the exact same thing you did on every chart. Just plot Brownian motion on a chart and do it, you'll see.

No you cant. If price drops below the red line it wouldnt be valid anymore. It would rather show an average direction, which is what you can REALLY do with every chart.

It would just be upside down. And I can choose a smaller interval to make it fit any way I want too.


Mobodick: It has more than one term because it doesn't begin at zero|zero.

[mobodick]

The explanation is you can derive some lower bond curve for every possible chart.

But could you then go on and describe this curve with one term?

It's not one term. And yes you can do the exact same thing you did on every chart. Just plot Brownian motion on a chart and do it, you'll see.

No you cant. If price drops below the red line it wouldnt be valid anymore. It would rather show an average direction, which is what you can REALLY do with every chart.

It would just be upside down. And I can choose a smaller interval to make it fit any way I want too.


Mobodick: It has more than one term because it doesn't begin at zero|zero.

It seems more likely that whatever caused this expansion simply started at that time and value and not at 0/0.
Remember that the price is a cummulative value many things influence it.

[ElectricMucus]

Well the thing is: People (including me) did that with a line on a exponential chart by drawing a line from this point straight up... that was back before the crunch. We were wrong.
This is just another iteration of the same fallacy: The belief that complex mechanics can be oversimplified and still be somewhat valid.

If we go below that curve you can simply scale that curve and have a new trend. Or somebody else comes along and makes it a polynomial or something. If we explode now in prices there will be other people who said they predicted that using some other mechanism.

Reality is different and to come up with a prediction over the next few months like you did you would need much more effort to have any more power than just random chance.

[Spekulatius]

The explanation is you can derive some lower bond curve for every possible chart.

But could you then go on and describe this curve with one term?

It's not one term. And yes you can do the exact same thing you did on every chart. Just plot Brownian motion on a chart and do it, you'll see.

No you cant. If price drops below the red line it wouldnt be valid anymore. It would rather show an average direction, which is what you can REALLY do with every chart.

It would just be upside down. And I can choose a smaller interval to make it fit any way I want too.


Mobodick: It has more than one term because it doesn't begin at zero|zero.

Hmm, I guess you are right. Too bad.

I still think may decreasing growth of value influx-theory has some substance, but it is probably applicable to a much larger time frame anyway. We are not even at 0.0001% of the potential value that may ever be converted into bitcoin. I therefore estimate the function of that particular growth to be very much at its beginning still.

The memory of traders seems to be also valid IMO, as evidence I would like to provide this graph here (switch to any time frame if you like):



The neighbouring areas of high volume seem to move up, never down (except for stark movements). From that I draw the conclusion that traders on average refrain from selling before their base price is not met. This way resistances and supports can be perfectly explained also.

[ElectricMucus]

Yes from what I have been able to research these glitches result from people aiming to hold a certain percentage of their assets in bitcoin and others aim to hold a certain percentage of total bitcoin or the ones on the market. The problem is they are totally unpredictable if you explain them that way.

There is however the tendency that they appear somewhat periodic.

[mobodick]

Well the thing is: People (including me) did that with a line on a exponential chart by drawing a line from this point straight up... that was back before the crunch. We were wrong.
This is just another iteration of the same fallacy: The belief that complex mechanics can be oversimplified and still be somewhat valid.

If we go below that curve you can simply scale that curve and have a new trend. Or somebody else comes along and makes it a polynomial or something. If we explode now in prices there will be other people who said they predicted that using some other mechanism.

Reality is different and to come up with a prediction over the next few months like you did you would need much more effort to have any more power than just random chance.

I'm not trying to predict the future, i'm trying to understand the past. And it seems that for two years there has been this consistent factor which acts as a barrier.
I'm also not so sure about it being a fallacy. It's pretty consistent so far and there is just no better way to describe the succession of low points. You could take points away from the right and it would still be roughly the same curve but with more error. So it seems to converge to this particular curve.
The error you get from having too little points where the bottom was hit made it possible for people to draw straight lines.

And the question is, why did the price fail to drop below this line during such a long period while lots of things happened to bitcoin.
What could be such a stable growing factor.
Another thing that fascinates me about it is that there are extended periods where the price 'scrapes' over the graph.

[pretendo]

People thinking it being tied to difficulty and mining equipment don't really have the whole story; the market accounts for future changes in bitcoin supply in the present price

[mobodick]

People thinking it being tied to difficulty and mining equipment don't really have the whole story; the market accounts for future changes in bitcoin supply in the present price

That might actually have a broad filtering effect over time.
Nice one.

[pretendo]

Well assuming an efficient market, immantenized prices would differ from future price points around the natural interest rate, that is, time preference. So the known increase in supply and increasing difficulty diffuses price increase out across time

[mobodick]

Well assuming an efficient market, immantenized prices would differ from future price points around the natural interest rate, that is, time preference. So the known increase in supply and increasing difficulty diffuses price increase out across time

Interesting proposal !

But somehow i still find it hard to imagine these factors would interact in such a way as to create such a mathematically simple evolution of minimal value as i have drawn.
To me it looks like it must have formed from some very simply related mechanism.
Or maybe, like Speculatius said, the graph is just not finished yet and will show a different term to the equation in the future.

If the curve would have become smooth becuase of time smear then i would expect the start of the graph to be smooth as well.
What we see in the graph, however, is that it seems to takes off pretty fast.
You can zoom in all the way to a month from the start and still be able to construct this curve and it defines the bottom still after more than 2 years.

Another thing is that if non-current price would be a big influence on current judgement then i propably could not have drawn this simple curve.
We've had bubbles where there was an unreasonably positive future component to speculaton and that should have pulled at this bottom.
What we see instead is that the bottom is the most stable, predictable part of bitcoin proce and all the action happens above it. There you can also clearly see the hype cycles.
I think that all speculation related activity lives above the line. The volume under the line seems a much more steady and hard component, almost as if it was built in.

Also, if there was an averaging effect i would expect it to live somewhere halfway between minimum and maximum price. Since the graph defines the bottom it seems to me that it is not composed of an average in any way at all. At the same time, there is no average graph that shows such a simple relation.
So i would rule out completely the idea that this graph is based on any averaging effects.
For the graph to be this simple and smooth the averaging effect over time must have been very big to be able to smooth out things like the bubbles but at the same time it must be small enough to form such a precise beginning.
I just don't think i can reconcile this into a one-term graph.

[TraderTimm]

Perhaps its the rate of US Dollar debasement

It is interesting, at any rate. Appreciate the effort, going to keep an eye on this.

[donking]

But the line theory is only valid if it starts at a particular date, october 8th 2010 or whatever it is.

What is so special about that date?

If you move the start of the line a month back it does not make any sense at all.

It sounds more like a case of a broken clock is right twice a day.

[mobodick]

But the line theory is only valid if it starts at a particular date, october 8th 2010 or whatever it is.

What is so special about that date?

If you move the start of the line a month back it does not make any sense at all.

It sounds more like a case of a broken clock is right twice a day.

I was wondering about the date as well.

But the clock analogy is pretty weak imo. It has nothing to do with this situaton.

The data before the effect starts is pretty horizontal.
Maybe it's some type of bifurcation function (only thing i can imagine with this kind of shape when the 'straight' beginning is calculated in) ?
In any case, there seems to be a clear tipping point right at that date.

Some potentially interesting thread:
https://bitcointalk.org/index.php?topic=749.0

[Spekulatius]

I agree, there may be some effects that keep the price from breaking below your function, since the USD/BTC exchange rate over time is no brownian motion, or random walk entirely dependant on coincidence.

Nevertheless what Electric Mucus said is still true, you can draw a function like that in every chart and run it forever. You only have to decrease the exponent over time as again and again your function will be broken lower.

What I question myself now is why that function is where it is right now, not higher or lower. It is not purely coincidence, because chart movement, as I understand it, consists of random events (like news) and predictable events (like reward drops) and traders reactions to that which on a large scale can be explained by mass psychology. Its not entirely random.
In contrast to traditional currency pairs, bitcoin currency pairs may actually inherit LESS variance (a measure for randomness distribution) due to their higher percentage of predictable events (like reward drops, bitcoin creation rate, mining factor, ..).

Also: your function is not totally accurate. It looks like your function has been broken a number of times already (if you wanna be really precise about it) in the beginnning, while price never touched it in the later half and rather hovered above it.

[mobodick]

I agree, there may be some effects that keep the price from breaking below your function, since the USD/BTC exchange rate over time is no brownian motion, or random walk entirely dependant on coincidence.

Nevertheless what Electric Mucus said is still true, you can draw a function like that in every chart and run it forever. You only have to decrease the exponent over time as again and again your function will be broken lower.

What I question myself now is why that function is where it is right now, not higher or lower. It is not purely coincidence, because chart movement, as I understand it, consists of random events (like news) and predictable events (like reward drops) and traders reactions to that which on a large scale can be explained by mass psychology. Its not entirely random.
In contrast to traditional currency pairs, bitcoin currency pairs may actually inherit LESS variance (a measure for randomness distribution) due to their higher percentage of predictable events (like reward drops, bitcoin creation rate, mining factor, ..).

Also: your function is not totally accurate. It looks like your function has been broken a number of times already (if you wanna be really precise about it) in the beginnning, while price never touched it in the later half and rather hovered above it.

If you want to look at it that way then the consequence is that you either add terms to your curve or you disregard the old points that do not fit your curve anymore.
But this graph shows that there is a series of points that live along this one-term line.
Seen from an earlier timepoint the future did not evolve like Mucus said! There is no case of finding a new point that messes up the old curve. Again, that is what makes it special. Since it's just one term it was like that from the beginning. No complexity was added during that time.
You could definitely NOT do this trick with a random dataset.
 

About my graph not being accurate.
That's true, it's a sketch and i would want to redo it with a bigger dataset.
But what you propably see is that price breaks the line in the beginning and hoovers above it later on.
That is just a question of tweaking the z parameter in the equation of the line (y=x^z).
Adjusting this number has exactly the right effect to correct for this discrepancy.
Remember that i was just creating these graphs in a graphing tool and just homing in on the right value for z.
After redoing it 3 times i tought it was ok enough

What would be left, i believe, after correcting this is the discrepancy around april 2011. I don't think there is a simple function that would touch this point.
But then again, all the other low points do match up...


I agree with you that this doesn't seem to be based on market behavior. It seems systematic to me.
There is something about bitcoin that makes it grow in value in this very steady way.

[Spekulatius]

If you want to look at it that way then the consequence is that you either add terms to your curve or you disregard the old points that do not fit your curve anymore.
But this graph shows that there is a series of points that live along this one-term line.
Seen from an earlier timepoint the future did not evolve like Mucus said! There is no case of finding a new point that messes up the old curve. Again, that is what makes it special. Since it's just one term it was like that from the beginning. No complexity was added during that time.
You could definitely NOT do this trick with a random dataset.
 

Take a look at this chart:



http://de.wikipedia.org/wiki/Random_Walk

x is time
y is deviation from 0
red line is standard deviation (it is expected with a certain chance that values stay in between the red lines.)

The graphs are a result of purely random input.

In a scenario where f(x) can never become Zero (like stocks and bitcoin), it is quite likely that the graph keeps climbing up for quite some time, till it comes down eventually (like the green one). So yes, you can do it with a random dataset.
The only thing that sets bitcoin apart from the above described is that bitcoin's exchange rate is NOT the product of pure randomness and may be influenced by some effects, for which we are looking for atm. Nevertheless is randomness an ingredient to the mix and will eventually produce an exchange rate that violates your bottom line. Other then in a random walk though, the chance for such event to occur may be significantly lower due to those unknown effects pushing the price up.

[mobodick]

If you want to look at it that way then the consequence is that you either add terms to your curve or you disregard the old points that do not fit your curve anymore.
But this graph shows that there is a series of points that live along this one-term line.
Seen from an earlier timepoint the future did not evolve like Mucus said! There is no case of finding a new point that messes up the old curve. Again, that is what makes it special. Since it's just one term it was like that from the beginning. No complexity was added during that time.
You could definitely NOT do this trick with a random dataset.
 

Take a look at this chart:



http://de.wikipedia.org/wiki/Random_Walk

x is time
y is deviation from 0
red line is standard deviation (it is expected with a certain chance that values stay in between the red lines.)

The graphs are a result of purely random input.

In a scenario where f(x) can never become Zero (like stocks and bitcoin), it is quite likely that the graph keeps climbing up for quite some time, till it comes down eventually (like the green one). So yes, you can do it with a random dataset.
The only thing that sets bitcoin apart from the above described is that bitcoin's exchange rate is NOT the product of pure randomness and may be influenced by some effects, for which we are looking for atm. Nevertheless is randomness an ingredient to the mix and will eventually produce an exchange rate that violates your bottom line. Other then in a random walk though, the chance for such event to occur may be significantly lower due to those unknown effects pushing the price up.

In your example none of the walks stay outside the red lines.
There is only a certain chance that they will be outside.
With the bitcoin chart the chance that the price will be above the line is untill now 100% and at the same time the price touched the line multiple times without going under.
You cannot compare that to the standard deviation of a random walk.
Your basically talking about means but means do not track the bottom.

I do understand that some random walk effect might exist and that if it grows large enough it could puncture the line. For now it seems there is no such effect. Bitcoin doesn't behave very much like a random walk so the random walk component, if there is one, must be (very) small.

[byronbb]

I wonder if the maker of this chart drives his destinations by using the patterns of the roads behind him

well I thought it was funny.

[Spekulatius]

If you want to look at it that way then the consequence is that you either add terms to your curve or you disregard the old points that do not fit your curve anymore.
But this graph shows that there is a series of points that live along this one-term line.
Seen from an earlier timepoint the future did not evolve like Mucus said! There is no case of finding a new point that messes up the old curve. Again, that is what makes it special. Since it's just one term it was like that from the beginning. No complexity was added during that time.
You could definitely NOT do this trick with a random dataset.
 

Take a look at this chart:



http://de.wikipedia.org/wiki/Random_Walk

x is time
y is deviation from 0
red line is standard deviation (it is expected with a certain chance that values stay in between the red lines.)

The graphs are a result of purely random input.

In a scenario where f(x) can never become Zero (like stocks and bitcoin), it is quite likely that the graph keeps climbing up for quite some time, till it comes down eventually (like the green one). So yes, you can do it with a random dataset.
The only thing that sets bitcoin apart from the above described is that bitcoin's exchange rate is NOT the product of pure randomness and may be influenced by some effects, for which we are looking for atm. Nevertheless is randomness an ingredient to the mix and will eventually produce an exchange rate that violates your bottom line. Other then in a random walk though, the chance for such event to occur may be significantly lower due to those unknown effects pushing the price up.

In your example none of the walks stay outside the red lines.

They do, up to a certain point.

There is only a certain chance that they will be outside.
With the bitcoin chart the chance that the price will be above the line is untill now 100% and at the same time the price touched the line multiple times without going under.

The red lines in the example are arbitrarily chosen. It means something in the tracks of "there is a 66% chance that the functions are in between the red lines at any given time", that chance could be increased or decreased at will to make the resulting function fit the bottoms of any chosen function.

You cannot compare that to the standard deviation of a random walk.
Your basically talking about means but means do not track the bottom.

No means that compute from past data like EMA, SMA,.. Those "means" if you want to refer to them like that, like in the above example are basically nothing else then a root functions like yours "y=x^(1/z)"

[mobodick]

If you want to look at it that way then the consequence is that you either add terms to your curve or you disregard the old points that do not fit your curve anymore.
But this graph shows that there is a series of points that live along this one-term line.
Seen from an earlier timepoint the future did not evolve like Mucus said! There is no case of finding a new point that messes up the old curve. Again, that is what makes it special. Since it's just one term it was like that from the beginning. No complexity was added during that time.
You could definitely NOT do this trick with a random dataset.
 

Take a look at this chart:

http://de.wikipedia.org/wiki/Random_Walk

x is time
y is deviation from 0
red line is standard deviation (it is expected with a certain chance that values stay in between the red lines.)

The graphs are a result of purely random input.

In a scenario where f(x) can never become Zero (like stocks and bitcoin), it is quite likely that the graph keeps climbing up for quite some time, till it comes down eventually (like the green one). So yes, you can do it with a random dataset.
The only thing that sets bitcoin apart from the above described is that bitcoin's exchange rate is NOT the product of pure randomness and may be influenced by some effects, for which we are looking for atm. Nevertheless is randomness an ingredient to the mix and will eventually produce an exchange rate that violates your bottom line. Other then in a random walk though, the chance for such event to occur may be significantly lower due to those unknown effects pushing the price up.

In your example none of the walks stay outside the red lines.

They do, up to a certain point.

No, they sort of randomly walk all over te place.
You cannot predict when or if they will hit the line.
And that is why you can only assign chance to a prediction.
And again, that is not how the bitcoinchart behaves.
You are trying very hard to make the bitcoin chart fit what you understand about random walks but it just doesn't fit the bill.
I dare you to graph the envelope of a random walk (whatever that is ) of the scale of bitcoin and call it a simple function.

There is only a certain chance that they will be outside.
With the bitcoin chart the chance that the price will be above the line is untill now 100% and at the same time the price touched the line multiple times without going under.

The red lines in the example are arbitrarily chosen. It means something in the tracks of "there is a 66% chance that the functions are in between the red lines at any given time", that chance could be increased or decreased at will to make the resulting function fit the bottoms of any chosen function.

Sure, so how would a 0% chance plot look in your case?
The bitcoin chart shows a line that represents (untill now) 0% chance of the price going there.
In your example there is no possibility for a 0% chance because all random walks will eventually cover all possible values.
So are you still comparing the same thing?
 

You cannot compare that to the standard deviation of a random walk.
Your basically talking about means but means do not track the bottom.

No means that compute from past data like EMA, SMA,.. Those "means" if you want to refer to them like that, like in the above example are basically nothing else then a root functions like yours "y=x^(1/z)"

Well, they are means away. Not like moving average tho. It's a mean of many random walks. So by doing lots and lots of random walks you can conclude that any particular random walk will be inside of the lines X% of the time.
If the bitcoin market was a random walk then it would be a single unique random walk and would just have a certain chance to be in certain places a certain amount of time.
To me the bitcoin chart seems completely unlike a random walk on a big scale and only a little bit on a small scale.
So to me this whole random walk thing is uninteresting as an explanation to my graph.

[wareen]

I wonder if the maker of this chart drives his destinations by using the patterns of the roads behind him

well I thought it was funny.

Yes, I had to smile as well, but if you think about it, that strategy would very probably outperform random guessing.
If you know very little about the forces that influence future behaviour, trend following is most often your safest bet.
Of course, trends or patterns can be found on any scale (just look at all the nice Elliot charts) and you can use trends to support just about any future extrapolation if you're really trying.

Having said that, very simple patterns are often seen and acted upon by many traders (at least here in Bitcoinland ). In some cases this leads to self-fulfilling prophecies - if there's a simple and often tested lower bound then it is not unreasonable to argue that this bound will hold, just because more people will start buying if the price drops near that bound. Of course, as soon as this lower bound exceeds the natural growth of the Bitcoin price it will eventually get broken, but for short term predictions such bounds can be valuable additional information.

So much for stating the obvious

I personally find the doubling of the price every 5 months starting from the 2011 November low of 2 USD to be such a rather simple and convincing lower bound. It was tested in June after which the price started to rise from 5 USD and tested again in August, "stopping" the pirate panic crash. I therefore consider a price above 16 in Jan/Feb 2013 a rather safe bet, but I wouldn't extrapolate it any further.

[fbastage]

In your example none of the walks stay outside the red lines.

If you start the red curve at some arbitrary non-zero starting point (non-zero on the x axis) you could very easily make one that "works".

I'm not saying your original post has nothing interesting in it, but the takeaway is mostly that "the minimum btc value has been increasing beyond some limiting function y for a finite range between x_0 and x_1". 

[mobodick]

In your example none of the walks stay outside the red lines.

If you start the red curve at some arbitrary non-zero starting point (non-zero on the x axis) you could very easily make one that "works".

I'm not saying your original post has nothing interesting in it, but the takeaway is mostly that "the minimum btc value has been increasing beyond some limiting function y for a finite range between x_0 and x_1". 

Exactly, but why would such a limiting function exist in such a simple form?
And i'll challege you too
Find a region in that picture with random walks that is limited to a one term function to this degree (so with multiple points touching the limit).
I don't think you'll find it.
I'd say it is so unlikely that what i found is not (for the most part) composed from this kind of behavior.
A random walk would (on average) keep on breaking its line but the bitcoin chart keeps confirming the line.
With a random walk all your one-term plots would have only 3 coresponding points, not 6 like in my graph, and not separated by these nicely formed bumps (notice there is very little structure to the triangles, it means they are not the result of a random walk. They would have looked more like mountain chains with multiple turnaround points if they were. This would also provide the basis for the 'forever able to make a new curve' thing.)

[fbastage]

Exactly, but why would such a limiting function exist in such a simple form?
...
I'd say it is so unlikely that what i found is not (for the most part) composed from this kind of behavior.

coincidence?  for the random finite period, it has worked.  if it didn't work for this period, it would have worked for some other period and some other function, given the multiplicity of possibilities.

I do think there have been SOME affirmative factors that aren't random, like increased adoption of bitcoin, but I wouldn't expect this specific minimum curve to hold for much longer.

And i'll challege you too
Find a region in that picture with random walks that is limited to a one term function to this degree (so with multiple points touching the limit).
I don't think you'll find it.

Maybe I'll give it a try later.