Bitcoin Forum

In this OP I will always post the last updated charts:

https://i.imgur.com/XnvT26Y.jpg

Nice graphics and nice work!  ;)

What software did you use?

-25% or -37% on the y-axis of the 1Bgn graph? The right and left axes disagree.

What price do you get in 2075? In my opinion the "equilibrium" price of Bitcoin is one of the easier numbers to make rational arguments about (thermodynamics is always on sounder footing than kinetics, etc.).
For example, if you get $1 trillion per BTC in 2075, I would say the model is problematic, however well fitted. If you get something in the $1-10 million range, then you're probably in the ballpark. (these models assume a certain optimism about adoption already)

Very interesting chart. I could definitely see BTC reaching $1k around April 2015 and then hovering around there until Q4 2015. The block reward halving will be a focus of discussion and I can imagine that topic causing a x10 increase to around $10k in late 2015. Guess we'll have to wait and see.

Probably about right.  ;D

But let's not forget the massive volatility we will have getting there!

In what year does your regression intersect with $1M USD?

Added to the OP:
Calculate today's trendline price HERE (http://www.wolframalpha.com/input/?i=10^%282.9065++*+ln%28%28number+of+days+since+2009+Jan+09%29%2Fdays%29+-+19.493%29)

Excel.

As Rpietila says, you can do amazing things with excel.

Your work is really great. This trendline seems realistic.

Could you provide a date for the one million dollar price ? Or extend your chart a little bit ?

Wow, nice work!
Thread watched and notified.
Just gave a small tip.

1.000.000 on 06-09-2026

I would like extend the chart to that date, but by excel worksheet doesn't want to. I don' know why.

What price do you get in 2075? In my opinion the "equilibrium" price of Bitcoin is one of the easier numbers to make rational arguments about (thermodynamics is always on sounder footing than kinetics, etc.).
For example, if you get $1 trillion per BTC in 2075, I would say the model is problematic, however well fitted. If you get something in the $1-10 million range, then you're probably in the ballpark. (these models assume a certain optimism about adoption already)

Nice post & analysis, Trolololo. Following.

I made a similar observation earlier this month in Stephen Reed's thread, about what looked like an increasing time span between reaching the next order of magnitude in network size, but didn't follow up on it (shameless plug to my own post :D (https://bitcointalk.org/index.php?topic=366214.500)).


A question.

I'm not sure about the exact type of growth of your function. What you seem to be mapping is logarithmic growth (slow) on a log chart (fast). Stripped of its minor constants, your formula is of the form 10^ln(t) for time = t. ln(t) grows extremely slow over time, but the result is used as a positive, growing exponent.

It seems to fall somewhere between linear growth and exponential growth, and it isn't bounded either (like in Stephen's model). I was wondering if someone with more knowledge on functional growth could answer this once and for all for me, have been wondering about this for a while now. (EDIT: I'm wondering if it could be an instance of so called sub-exponential growth)


A critical remark.

While I personally, intuitively, find a price function with a declining growth rate (like yours) more plausible than the constant growth rate models that have been presented on this forum (i.e. the "loglinear models" you linked to as well), one problem still remains:

Price tends to "jerk around" all those models.

I remember that, late last year, when price exceeded even the loglinear model's predictions, some analysis was posted that suggested a superexponential price function to model BTC price.

Then came the first leg of the 2013/2014 correction, and suddenly the loglinear models were all the rage again.

Now, the correction continues, and you suggest (with good reasons, I agree) a model based on an below exponential growth assumption. But I'm afraid all it takes is another year of bear market (or perhaps, a sudden rally of huge proportions), and we need to re-adjust our assumption for what the "best" growth type for our model is...

Here's what I'm trying to say: I am using technical (i.e. historic price based) methods myself all the time for predicting price on the short term. However, I start to think that, on a long enough time scale, fundamentals govern the price function. So a model like yours (or Stephen's, or rpietila's), that are essentially an extrapolation from an (admittedly well fitted) function on the historic price data might come to its limits.

I am thinking that perhaps the only semi-reliable way to go about mapping the "long term trend" is Peter R.'s way: finding a proxy for network size, and then modeling expected price/mcap as a function of network size.

See for example here: https://bitcointalk.org/index.php?topic=68655.msg9059346#msg9059346

He still makes a number of assumptions (Metcalfe's law, for example), and in a way, his method only shifts the problem (because now we are trying to predict, i.e. extrapolate, network size), but at least his predicted numbers will rarely be so out of tune with reality as the pure time series models can be at times.

Edit: no "S" look at all. Looks like a "lowering" exponential trend for any timeframe.
To have a "S" look que should use another regression function, like
http://upload.wikimedia.org/math/1/b/2/1b220293537440836b386dc1a3ff7a7b.png

I remember that, late last year, when price exceeded even the loglinear model's predictions, some analysis was posted that suggested a superexponential price function to model BTC price.

nice charts :)

will folow your posts from now on

edit: left you a small tip :)

Excel.
As Rpietila says, you can do amazing things with excel.

I'm not sure about the exact type of growth of your function. What you seem to be mapping is logarithmic growth (slow) on a log chart (fast). Stripped of its minor constants, your formula is of the form 10^ln(t) for time = t. ln(t) grows extremely slow over time, but the result is used as a positive, growing exponent.

10^ln(x) = x^ln(10)

In what year does your regression intersect with $1M USD?

Thanks. Feel like an idiot for missing that.

Which would make it about quadratic growth. Interesting.

In this OP I will always post the last updated charts:

Calculate today's trendline price HERE (http://www.wolframalpha.com/input/?i=10^%282.9065++*+ln%28%28number+of+days+since+2009+Jan+09%29%2Fdays%29+-+19.493%29)

Great work Trolololo.

Can't see it mentioned yet, maybe it is elsewhere, but do you have a version which utilizes the "market capitalization" (monetary base), instead of the price? For the first decade this may produce a somewhat different curve.

Thanks for your acknowledgments!
I truly appreciate all your comments (and tips  :))



No, Risto also suggested that, but I don't have any "market capitalization" version yet.

Actually working on calculating the "real" R^2 value for the logarithmic regression, and in other curve shapes...

Yes I thought so too. If you buy the Metcalf's Law valuation argument (I don't entirely), that corresponds roughly with linear growth of usage. Which interestingly is what Chris Dixon has said they are seeing in his businesses (mostly Coinbase I think).

Hello everybody,

I'm pretty new to bitcoin, looked first at it this summer.  I also did some curve fitting to the historical data in log scale.  Of course, one has to be extremely cautious when extrapolating from early price movements, but intuitively the idea that the bitcoin price should "do something" is pretty clear.  I'm cautiously also buying modest amounts of bitcoin... for my retirement in a few decades, based upon similar extrapolations.

When looking at the long term (and not doing day trading), one must always look at the fundamentals.  Now, bitcoin is supposed to be a monetary asset, in the same way as fiat, or as physical gold: it doesn't serve any other purpose but as "money", that is, intermediate vector of value.  A monetary asset is in a certain way a "frozen Ponzi scheme" or a "frozen bubble" to some extend in my opinion: the only reason why you give it value today (why you want to spend real effort and other monetary assets on it) is that you believe that someone else will estimate it has value tomorrow, and that you will get something for it in return.
Shares, houses, and other investments also have a part of "monetary asset", but they usually also have another cash flow associated to them, like dividends, rent or usage (you can *live* in a house), so there is a "floor" to their price, which is their cash flow or usage.  Gold has a very limited "usage" in jewels and so on, but is essentially a nearly purely monetary asset.

Now, for a purely monetary asset, its "value" is solely determined by the "quantity theory of money", which states that in steady state:
P x Q = M x V

where P is the price of goods, Q is the quantity of goods bought with the monetary asset, M is the amount of monetary asset, and V is the average velocity of the monetary asset.

The "price of a bitcoin" B is then 1/P, and we have:

B = 1/P = Q / (M x V)

So you can expect the price of a bitcoin to be the amount of stuff (expressed in dollars) divided by the amount of bitcoin in circulation M, and divided by the velocity V.

Now, 1/V is given by the "(harmonic) average holding time" of a bitcoin between two buys, which we can call T.

We hence have:

B = Q x T / M

Or: the market capitalisation is B x M = Q x T

In other words, the market capitalisation is grossly given by the value of all stuff bought with bitcoin, times the (harmonic) average hold time of a bitcoin.

Many expectations of "too the moon" are based upon a similar "holding time" T for fiat and for bitcoin: in that case, the market capitalisation is then comparable to the fraction of the fiat market capitalisation that is done in bitcoin.

......

Hello everybody,

I'm pretty new to bitcoin, looked first at it this summer.  I also did some curve fitting to the historical data in log scale.  Of course, one has to be extremely cautious when extrapolating from early price movements, but intuitively the idea that the bitcoin price should "do something" is pretty clear.  I'm cautiously also buying modest amounts of bitcoin... for my retirement in a few decades, based upon similar extrapolations.

When looking at the long term (and not doing day trading), one must always look at the fundamentals.  Now, bitcoin is supposed to be a monetary asset, in the same way as fiat, or as physical gold: it doesn't serve any other purpose but as "money", that is, intermediate vector of value.  A monetary asset is in a certain way a "frozen Ponzi scheme" or a "frozen bubble" to some extend in my opinion: the only reason why you give it value today (why you want to spend real effort and other monetary assets on it) is that you believe that someone else will estimate it has value tomorrow, and that you will get something for it in return.
Shares, houses, and other investments also have a part of "monetary asset", but they usually also have another cash flow associated to them, like dividends, rent or usage (you can *live* in a house), so there is a "floor" to their price, which is their cash flow or usage.  Gold has a very limited "usage" in jewels and so on, but is essentially a nearly purely monetary asset.

Now, for a purely monetary asset, its "value" is solely determined by the "quantity theory of money", which states that in steady state:
P x Q = M x V

where P is the price of goods, Q is the quantity of goods bought with the monetary asset, M is the amount of monetary asset, and V is the average velocity of the monetary asset.

The "price of a bitcoin" B is then 1/P, and we have:

B = 1/P = Q / (M x V)

So you can expect the price of a bitcoin to be the amount of stuff (expressed in dollars) divided by the amount of bitcoin in circulation M, and divided by the velocity V.

Now, 1/V is given by the "(harmonic) average holding time" of a bitcoin between two buys, which we can call T.

We hence have:

B = Q x T / M

Or: the market capitalisation is B x M = Q x T

In other words, the market capitalisation is grossly given by the value of all stuff bought with bitcoin, times the (harmonic) average hold time of a bitcoin.

Many expectations of "too the moon" are based upon a similar "holding time" T for fiat and for bitcoin: in that case, the market capitalisation is then comparable to the fraction of the fiat market capitalisation that is done in bitcoin.

If bitcoin becomes a success, in the sense that, world wide, people buy and sell stuff in bitcoin, then this market capitalisation can be potentially huge.  Only in dollars, there are 2 - 10 trillion dollars in circulation.  World wide, the estimate (M2 money) is of the order of 55 trillion.
If bitcoin would take 1% of the world trade, its market cap would be about 550 billion dollars.  If bitcoin doesn't even buy 1% of stuff in the world, then the question can be asked whether it made sense in the first place to consider it as a monetary asset.

That is, under the assumptions of similar average hold times.

So that's about a 100-fold increase in market cap compared to now.

Essentially, this is the "amount of value" one needs bitcoins to have in order to be able to buy all that stuff, and to hold all those coins for a time T.

The crucial point is T: if people would just buy bitcoins (with fiat) to spend them immediately, then T becomes much shorter than the average hold times.  This can pretty much lower the market cap needed to buy all that stuff.  Essentially, if bitcoins are only held "a few seconds" the time to buy them with fiat, and to spend them buying some goods, you see that the market cap of bitcoin would be extremely limited.  If 1% of goods are traded in bitcoin, but bitcoins are held 100 times less long than fiat, then market cap is not going to change !

But bitcoin has promises as a store of value too, so chances are that people will actually hold on bitcoin also as "store of value".  Even more so than to fiat which has a bad reputation as store of value.  That might actually make T *longer* than the T of fiat.

However, for the moment, I have no idea, but Q is pretty low (except maybe on black markets, which do play a role in the early phases of bitcoin).

So why is bitcoin then worth something ?  I think we are still in a hugely speculative phase, where the current price of bitcoin is more the future *expectation* of what its price will be, rather than the actual value in monetary use.  Most people (like me) speculate somehow that bitcoin is going to become a success, and that people will not only use it to buy stuff (Q), but also as a store of value (T). 

This has the potential to put the bitcoin price B pretty high.

But it won't happen overnight.  You are not going to wake up, with people buying suddenly 1% of the world economy in bitcoin.   This is going to be a slow process, and to me, *this* is the fundamental value of bitcoin.   The current prices are short-term effects of traders, and the longer term consists in the long term belief of high bitcoin value, that is, a long term speculation on the value of B, as a function of Q and of T.

It can also be that bitcoin flops.  But for the moment, I'm taking a prudent bet on "to the moon", but over a decade or more.  It would be a nice complement to my retirement. 

However, in my opinion, there's no fundamental which can support a "to the moon and staying there" in the near term: Q is too low for the moment.  For bitcoin to become money, you have to buy a significant part of the world economy with it (1% is a very "significant part").

What is dangerous with curve fitting, is that there will be a transition at some point, from the "speculative" domain where we are in now, to the "monetary domain" when it is really on its monetary fundamentals.  There's no reason why fitting laws on the speculative part should have anything to do with the monetary circumstances.

person talking sense

thanks for the great insight.

I always thought that the quantity theory of money would fail to deal with the store of value function of money (or hodling) assuming that money is always neutral.

You seem to have a deeper understanding of that - so I have a few questions:

1.) I think that bitcoins function as a store value will for quite a long time be more important than its usage (even though being interdependent). Can you give more insight regarding factor T? Or provide a good (academic) article regarding that factor in this particular kind of analysis in QTM?

2.) It is obvious that the price is hugely driven by speculation - but given todays market capitalization (~5 Billion) we could say that it shows (no one knows if this is really possible on methodological level) that we give it a 1 % chance to get 1 % of the trade and store of value of the world economy (500 Billion). or do I misunderstand that?

3.) I always have the assumption that we as economist fail when time comes into play ;). But you tried to give some insight regarding that, when you say that you do not think that it will be an overnight ride to the moon and assume that it takes a decade. But let us simply assume that perception regarding bitcoin changes due to some factors. At question 2 we had a 1% chance at todays prices to reach 1% of the world market. for simplification let us assume we change to a 10% chance. Don't you think that prices would climb much faster, even given the same or nearly the same velocity?

4.) given your formula. Do you think it is possible to fill it with numbers, to give us a speculation free price of bitcoin - I think I do not completely get your factor t and how to use it.

I suspect that in the very long term (reaching year 2075 i.e.) the linear price axis graph would look like an "S" curve (logistic growth). Pending task...

Bitcoin logarithmic regression with inverted and scale dollar index on it.
http://www.everego.com/btc-dxy.jpg

In this OP I will always post the last updated charts:

Calculate today's trendline price HERE (http://www.wolframalpha.com/input/?i=10^%282.9065++*+ln%28%28number+of+days+since+2009+Jan+09%29%2Fdays%29+-+19.493%29)

https://i.imgur.com/XnvT26Y.jpg

https://i.imgur.com/qyZFE4o.jpg

Nice! Thanks for the update, @lesni4ok.
Could be interesting to build that charts on an online-system that updates automatically and let everyone check in real-time  ;) Don't you think so?

I don't know if there's something similar  :D

Plotting a best fitting line through a time series makes no statistical sense. [...] Another problem that I also discuss is that model parameters change over time.

Paging a statistics expert prepared to defend the use of the ordinary least squares method.

A little patience is really all that is required here. This model is calling for 1000 USD/BTC in three months or so. Sooner or later the price will either converge with the model or will diverge so much that the model becomes absurd. So far neither has happened.

There is a certain structural validity to it, if you accept Metcalf's Law as a valuation metric and observe that users have been growing roughly linearly (reported by coinbase and others).

Agreed, certainly seems we where ahead of the curve during the last ATH.
Would be nice for some updated charts covering into 2015 ....

A little patience is really all that is required here. This model is calling for 1000 USD/BTC in three months or so. Sooner or later the price will either converge with the model or will diverge so much that the model becomes absurd. So far neither has happened.

There is a certain structural validity to it, if you accept Metcalf's Law as a valuation metric and observe that users have been growing roughly linearly (reported by coinbase and others).

Arg, where's that article on Metcalfe's Law being wrong... I feel (vague, I know, I know) like it's more n log(n) than n^2.

Eh, maybe n^2 is the better model during early growth, though.

Can you please post an update to this?

Great work Trolololo.

Can't see it mentioned yet, maybe it is elsewhere, but do you have a version which utilizes the "market capitalization" (monetary base), instead of the price? For the first decade this may produce a somewhat different curve.

It's interesting how an updated regression, in a situation where the price has been going down, and with a reportedly "fairer" R2 fit, that it would end up projecting *higher* prices than the original. That said, I do appreciate your contributions.

There has been so much divergence that to update it now would just look ridiculous.

He will update it when the price rises to be more in line with his predications.

If anyone knows how to execute a "Solve" like command in a Google Datasheet, I'm all ears...

According to your chart we should have reached 1000 by now! :D

But really, if you're right, we've got a long way to recover...

According to the log regression's trend, 1182 is today's estimated value.

You can see it here (http://www.wolframalpha.com/input/?i=10%5E%283.1737++*+ln%28%28number+of+days+since+2009+Jan+09%29%2Fdays%29+-+21.424%29).

So the price is 76% undervalued.

i am thinking that the 1MB limit is increasingly becoming a dead-weight on the value. This roadblock to scalability is highly publicized now, and it is reasonable that large amounts of money is on the sidelines waiting to see whether Bitcoin can properly scale. The sooner v4 blocks are happening the better the environment will be for the value to return to trend.

Are the debates on this done? There were half people that said yes and the other half said no. Is it decided for sure then?

I have a question to the OP: what are the underlying assumptions that make this log regression's trend held over the entire period depicted?
It is hard to believe, taking out some severe doom-like event to the US dollar, to see the price of Bitcoin reaching $100k by 2020. Not even to talk about the valuations beyond the 2020. Isn't it that you try to estimate the trend for much longer time period (next 10, 20, 50 years), having the data from a relatively short period of time (2010 till now) and thus committing a huge prediction error, due to the insufficient amount of data?

As said before, this log regression just tries to have a better estimation of bitcoin's value than the linear one. Specially for a 2 or 3 years horizon.

For a longer term value, it's worth to take a look at James d'Angelo's "Bitcoin Price Model (http://worldbitcoinnetwork.com/BitcoinPriceModel-Alpha.html)".

I know that this is your time window, but still my question that remains unanswered is: do you have enough data so far, to make such regression reliable?
So far you had like 2081% above the line and 81% to the downside, which indicates that the fit to the curve is far from acceptable in terms of prediction error. Meaning probably you don't have enough 'training data' to make any reliable predictions for the future.
Just to illustrate what I am talking about, try a small exercise: take only first two years of data and make the regression based on that. Compare that to the real results in terms of errors. You will probably see even worse results in terms of how far it is from reality.

This is an interesting way to approach the 'real' price of Bitcoin... I've seen many people do similar things. I guess one of the most prominent being rpietila, you know the guy with the castle and the pink car. Haha, man... he's awesome!

He predicted 1 Million per coin back then. I wonder where does he stand nowadays and if he still believes that will happen and when.

Unless you're willing to propose some sort of non-standard regression function that makes sense as applied to the Bitcoin market, complaints about 2081% and -81% are unfounded here. The fact that the Bitcoin market has volatility with respect to the regression trend does not mean that this chart offers nothing worthwhile in terms of representing reality. To get an equation to follow the price more closely, you'd have to throw in something more exotic, like an oscillation component or something, and doing so just to get a better fit is often not the best tactic.

I have a question to the OP: what are the underlying assumptions that make this log regression's trend held over the entire period depicted?
It is hard to believe, taking out some severe doom-like event to the US dollar, to see the price of Bitcoin reaching $100k by 2020. Not even to talk about the valuations beyond the 2020. Isn't it that you try to estimate the trend for much longer time period (next 10, 20, 50 years), having the data from a relatively short period of time (2010 till now) and thus committing a huge prediction error, due to the insufficient amount of data?

I understand that the idea is to have something very simple and non-complex to approximate the price of Bitcoin, but still I feel uneasy (even very uneasy) when I see the prediction error and the number of data samples on which the trend is based. And I believe that is perfectly founded complain, to which I haven't got any response yet, rather than that one regression is better than the other (linear one). What if both are not closely enough approximating the trend?
Now, you also say that it makes a perfect sense to use such a regression. Can you explain in more detail, what backs that statement?

If the guys making the charts could actually predict the market movements, they'd be rich

I don't think more samples would make it more accurate for forecasting. This isn't something where we are lacking data points. What we've got is the best that we can have. You could use intra-day data for more samples, for example, but that wouldn't help anything; the daily weighted price is fundamentally representative of that.

Assumptions have to be made. Trolololo has made some. It's likely that the information necessary to best predict the price may not solely be contained in the past price data. Keep in mind, price growth can't just continue forever. But determining what outside parameters may predict where the model will diverge from a particular pattern is a hard question.

Read through the following for some formal assumptions and interpretation: https://en.wikipedia.org/wiki/Linear_regression#Assumptions

Also, the following:

Edit:

The following is also helpful: https://en.wikipedia.org/wiki/Overfitting

If you take the regression on the very first few seconds before the stone starts falling, you would probably see a very different curve, than what you would plot if you have a longer time window.

He claims he dumped a lot of his bitcoins for monero. He may have been pumping and dumping.

I personally think Bitcoin is undervalued in the long term, but I'm very curious and interested to see what happen in 2015

He did, but he's only pumping Monero, not dumping it. :)

I think altcoins breaks that theory cuz they reduce people interests to bitcoin.

Yeah that was really puzzling me, seeing someone like him really falling for an altcoin. If any crypto succeeds it will most likely be Bitcoin, there's no reason to invest in anything else - it really is just exposing you to more risk.

Trolololo thanks for the charts. Are you interested in releasing the spread sheet so that we can easily update the spread per your formula?

Since some days ago we are in record undervaluation: -81%

Trolololo thanks for the charts. Are you interested in releasing the spread sheet so that we can easily update the spread per your formula?

Hi, Lord Oliver

1.- The resulting parameters would be almost identical. Dollar and gold relationship is very stable compared to bitcoin...

2.- The logarithmic function is quite nice for a medium term horizon (1 or 2 years from now) and it's much better than the linear one.
But it's not as accurate in the long term. As I have stated in former posts, I would prefer an asymptotic function for the long term.

Regards.

Please, Sirs, let's keep this thread clean.

There are other threads to talk about Risto or/and Monero or/and any altcoin vs bitcoin.

Thank you.

Requesting updated chart since last one did in May 2015.

two weeks went by and no response?

Is this thread still alive?

Forecasting is totally useless. Based on currently available date you get this result by 2020
https://i.imgur.com/r0utGyM.png 
The past will not tell you the future

 
  
Trolololo, I don't know if you know me or not, but I'm a big fan.  How much of a donation would it require to get you to create a chart like this for Monero? (even though I know we only have a year of history to go off of)

https://i.imgur.com/5RJcLZ3.png
As i sad before the past does not tell the future.

To have different starting dates on one forecast chart does not work. So  here is a fix. Not that is really meaningful. The other issue is the missing early data for bitcoin, it is needed so i started a one cent.
https://i.imgur.com/UGHmikz.png

Who's to say that starting the bitcoin price at one cent is meaningful? :)

although I think the idea is good, the numbers seem off by a lot.

I don't think bitcoin will stay at or below $1000 for that long.

based on this chart, it would seem bitcoin would stay around $1000 far into 2020, which is completely ridiculous.

I will upload chart asap.

Hello all, I'd like to share my previous chart on tradingview
https://www.tradingview.com/chart/BTCUSD/VKWhgBho-Cup-and-handle-pattern-for-Bitcoin/

Could u update Trolololo?  8)

Chart update!!

Chart update!!

In this OP I will always post the last updated chart:

Update 2017-01-03:
https://s27.postimg.org/illwa70gz/logarithmic_03_01_2017.jpg
Donations: bitcoin:1Fe6B3Zo4HxaCD8ybi9A8zBRH2wKpciUxe

Calculate today's trendline value HERE (http://www.wolframalpha.com/input/?i=10^(2.66167155005961++*+ln((number+of+days+since+2009+Jan+09)%2Fdays)+-+17.9183761889864))

Chart update!!

https://s27.postimg.org/illwa70gz/logarithmic_03_01_2017.jpg

Today's theoretical value (check HERE (http://www.wolframalpha.com/input/?i=10^(2.66167155005961++*+ln((number+of+days+since+2009+Jan+09)%2Fdays)+-+17.9183761889864))) is around 2100 USD, so the price is half undervalued.

Please, consider donating to bitcoin:1Fe6B3Zo4HxaCD8ybi9A8zBRH2wKpciUxe

@Trolololo
I have another suggestion. Can you try to do this for the market cap instead? This should be a little more precise as its flattening out the early parts a little

Actually, Trolololo, could you make one for the total marketcap of all coins?

Let me know for how much you can do this? I'm very happy to pay for this to get this done as soon as possible.


The one thing I think these calculations overlook is that other cryptos can take over the market from bitcoin and so past growth trend may not be extrapolated into the future. This has also just happened I think due to the black swan event of bitcoin not being able to process anymore transactions for half a year now. However for the whole cryptocurrency market this is still valid, but if u were to make such a chart I think you would see that current marketcap of all cryptos is already considerably above it's expected average and is due for a correction, and therefore Bitcoin as well, eventhough it is not yet way above it's expected price.

Chart update!!

https://s27.postimg.org/illwa70gz/logarithmic_03_01_2017.jpg

Today's theoretical value (check HERE (http://www.wolframalpha.com/input/?i=10^(2.66167155005961++*+ln((number+of+days+since+2009+Jan+09)%2Fdays)+-+17.9183761889864))) is around 2100 USD, so the price is half undervalued.

Please, consider donating to bitcoin:1Fe6B3Zo4HxaCD8ybi9A8zBRH2wKpciUxe

Trolololo, only recently discovered this amazing work - THANK YOU (and others).

I did a bit of my own work in Excel and came up with this chart, which I think is fairly close (based on 1st of the month values in CoinMarketCap). (...)
I then made a monthly chart for BTC for the last 2.5 years and like the correlation.

But I have to confess I don't completely understand the values for 10 ^ 2.66167155005961 as well as the -17.9183761889864? Could you potentially elaborate or point me in the right direction?

Reason been - I tried to evaluate ETH and had to move the START DATE from 9-JAN-2009 (for BTC) to 1-JAN-2013 (ETH?) to get an "acceptable visual correlation" (not very scientific I know). This is my best guess at the moment...

Actually, Trolololo, could you make one for the total marketcap of all coins?

Let me know for how much you can do this? I'm very happy to pay for this to get this done as soon as possible.


The one thing I think these calculations overlook is that other cryptos can take over the market from bitcoin and so past growth trend may not be extrapolated into the future. This has also just happened I think due to the black swan event of bitcoin not being able to process anymore transactions for half a year now. However for the whole cryptocurrency market this is still valid, but if u were to make such a chart I think you would see that current marketcap of all cryptos is already considerably above it's expected average and is due for a correction, and therefore Bitcoin as well, eventhough it is not yet way above it's expected price.

Suggested topic is devoted to discussion of Global Road Map of Bitcoin BTC



Based on following factors (I-IV) suggested for discussion is the Bitcoin Global Road Map (V).


I Number of active bitcoin wallets

According to Mr.Woo's http://woobull.com/woos-law-of-bitcoin-user-growth-bitcoins-adoption-curve/ research, bitcoin users double every 12 months. Mr. Woo makes corrections (S curve) based on real world human behaviour. Here comes wild idea that algorythms, based on mathematics and Laws of Universe are already changing real world human behaviour. Through smartphones, computers and gadgets they force us to move quicker to live more intense lives. They change us, attuning human schedule to Rythms of Universe, hence increasing people's efficiency.



II Halvings schedule (next is on June 12 2020) - recalculating of network difficulty

The network started on January 3 2009. First halving took place in 2012 which led to all time high of more than $1000 in November 2013. So, after halving bitcoin price can increase 10 fold. After next halving in 2016 we witnessed the power of third wave of bitcoin evolution in November 2017, when bitcoin rocketed to $7,900 and peaked $12,400 in Zimbabwe.
After next halving, which means that emission of bitcoin slows down and miners will be rewarded only 6.25 bitcoins (now 12.5) for one mined block. Which increases the cost of every mined coin. Because of the limited coins supply increases the price.


III Achievements of past 9 years of bitcoin existence

https://99bitcoins.com/bitcoinobituaries/ 183 times Bitcoin could die. No other technology/product/startup is known that could survive under such huge pressure. That shows mathematical correctness of the protocol, flexibility and stability of Bitcoin Protocol. That means Bitcoin can evolutionate. It can change. Like a snake that gets rid of old skin, bitcoin is moving further, leaving its forks behind. Open to whole world's pressure, represented by banks, governments and financial institutions from outside and numerous challenges in form of soft and hard forks from inside, Bitcoin became capable to digest these pressures in the process of becoming holistic (i.e. indestructable) technology.

The Bitcoin Technology (Protocol) is so advanced and multifaced (combined knowlegde from Game Theory, Economics, Programming, Finance, Cryptography, Quantum Mechanics) that still there are only a few people who completely understand this technology. Since the Bitcoin building is so huge, some people see only separate floors of this building. Some see financial implications. Some see social implications. Some see that this technology can change the world completely - there will be no need in banks, governments, Systems. Some see the future of the technology in VR and IOT. Some call it digital gold. Some - digital currency. Some - digital assets. Probably we see birth of new class of asset, to which quite another approach should be taken by regulators. It is nither currency nor goods. It is all together, all kinds of assets represented in one digital form.  
The Technology is self-balancing, coming to dynamic equilibrium from any internal or external impulse, be it soft/hard forks or governmental pressure/attacks, between 4-5 parties, such as Developers, Wallets (People interacting with this technology), Finance (financial institutions, institutional investors), Miners and IoT in the future (yes, the Robots). Bitcoins can be traded 24x7, time moves 20 times faster in the world of Bitcoin, which can accelerate growth of human economics.



IV Hello New World !!!!

Bitcoin technology gives you freedom. Independence. But it also has another side of the coin - Responsibility. Personal. You are responsible for your money and if you were not conscious building cryptocurrency portofolio you can loose your funds. If you transfer to wrong address, you can't undo. No banks can help. No insurance company. You bear all the risks.
That increases awareness. That leads to forming many people making decision to take their Fate into their own hands. To be independent from the governments and banks. To have their own opinion how to live their lives. That means new way of living. No borders. Decentralised education, stimulating people to think independently to make decisions by themselves. Probably there will be merging of old (centralized) and new (decentralized) approaches in the world. Decentralization (New World) offers Competition to old centralized world, which can lead to mutual growth in the dance of Evolution.



V Bitcoin Global Road Map

---------------------------1 Birth of Bitcoin---------------------------

2007            Bitcoin Design and Coding
2008            October - White paper published

---------------------------2 Bitcoin's childhood------------------------

2009 Year 1. January - genesis (first) block mined. Year 1 (started from October 31 2008)
2010 Year 2. Bitcoin exchanges and bitcoin exchange rate established
2011 Year 3. Satoshi Nakamoto leaves the project, as it became self-sustainable
2012 Year 4. First Halving.
2013 Year 5. November $1000 peak
2014 Year 6. Massive correction  
2015 Year 7. Gaining stability
2016 Year 8. Second Halving. Segwit
2017 Year 9. Segwit 2x.
                   Around 0.2% of people (10-15 mln) using Bitcoin  
                   80% of coins mined.
                   Global acceptance among institutional investors.
                   By the Year 10 (November and December 2017) all time high $7,900

---------------------------3 Sky (Bitcoin's adulthood )--------------------------

2018 Year 10. $14,000-$27,000 (Fifth wave by Elliot)
2019 Year 11. Technologies such as Lightning Network (momentary payments, no 10 min waiting) are implemented in
                      the second layer of Bitcoin protocol.
                      Next Segwit 3.
                      Around 1% of people using Bitcoin.
                      Massive correction (50%+)
2020 Year 12. Third Halving.
                      Around 2% of people using Bitcoin.
                      Recovery and movement to 6 digits.
2021 Year 13. Around 4% of people using Bitcoin.
                     This year we will see 6 digits.
                     $100,000 per Bitcoin
2022 Year 14. Around 7% of people using Bitcoin.
                     Consensus with banks and governments - they Must Change to Survive.
                     Bitcoin wons this competition and banks/governments are forced to demonopolize themselves and change
                     their Attitude - State is People's Servant. State has to Serve People.  
2023 Year 15. Around 12% of people using Bitcoin

------------------------4 Space (Bitcoin's maturity) -------------------------------------

2024 Year 16. Fourth Halving?
                     Around 25% people using Bitcoin.
                     Blockchain technologies massively implemented
2025 Year 17. $1 Mln per bitcoin.
                     50%+ people using Bitcoin.
                     Bitcoin goes into Space (literally, to Mars).
                     Blockstream orbital sattelites broadcast bitcoin transactions worldwide and in the entire Solar System.
                     Technologies such as Atomic Swaps are implemented in top cryptocurrencies.
2026 Year 18. Segwit 4.
                     Massive correction.
2027 Year 19. Recovery.
2028 Year 20. Fifth Halving? 80%+ of people using Bitcoin.
                     Over $10 mln per bitcoin.
                     Irreversable changes (80 - 20 Law) in Human Society driven by Bitcoin technology.
                     Social changes.
                     Change in System of Values of Man.

------------------------- 5 Hello New World---------------------------------------------------

2032 Year 24. New generation (since 2012) is formed.
                     Total acceptance of bitcoin by all people.
                     Total death of fiat money.
                     With the evolution of AI possible human race economics growth up to 10 times.
                     $100 mln per bitcoin.
                     1 satoshi = 1 usd.
                     2,000 trillion dollar human race economics (now equals to 70 trillion dollars ) potential growth (AI, IOT,
                     Space industry etc.)
 

Trolololo, here is the Vision (Road Map 2017-2028) of Bitcoin future. The key figures correlate to your chart. Thank You.


Taken from another topic.

Trolololo, here is the Vision (Road Map 2017-2028) of Bitcoin future. The key figures correlate to your chart. Thank You.


Taken from another topic.

Chart update!!

Today's theoretical value (check HERE (http://www.wolframalpha.com/input/?i=10^(2.66167155005961++*+ln((number+of+days+since+2009+Jan+09)%2Fdays)+-+17.9183761889864))) is around 2100 USD, so the price is half undervalued.

Please, consider donating to bitcoin:1Fe6B3Zo4HxaCD8ybi9A8zBRH2wKpciUxe

In this OP I will always post the last updated chart:

Update 2017-01-03:
https://s3.postimg.org/kmzui60kj/logarithmic_03_01_2017.jpg
Donations: bitcoin:1Fe6B3Zo4HxaCD8ybi9A8zBRH2wKpciUxe

Calculate today's trendline value HERE (http://www.wolframalpha.com/input/?i=10^(2.66167155005961++*+ln((number+of+days+since+2009+Jan+09)%2Fdays)+-+17.9183761889864))

ok, we are pointed to 100l in three years?? fine I'm ready to ride
but I'm sure there would be huge corrections  and humps during this flight to 100k
are you guys ready?

Amazing, Nostradamus like stuff  ;D

Very good predictions, I´m impressed.

In this OP I will always post the last updated chart:

Update 2017-01-03:
https://s3.postimg.org/kmzui60kj/logarithmic_03_01_2017.jpg
Donations: bitcoin:1Fe6B3Zo4HxaCD8ybi9A8zBRH2wKpciUxe

Calculate today's trendline value HERE (http://www.wolframalpha.com/input/?i=10^(2.66167155005961++*+ln((number+of+days+since+2009+Jan+09)%2Fdays)+-+17.9183761889864))

People should donate to him. Hopefully he still controls the associated wallet.

In this OP I will always post the last updated chart:

Update 2017-01-03:
https://s3.postimg.org/kmzui60kj/logarithmic_03_01_2017.jpg
Donations: bitcoin:1Fe6B3Zo4HxaCD8ybi9A8zBRH2wKpciUxe

Calculate today's trendline value HERE (http://www.wolframalpha.com/input/?i=10^(2.66167155005961++*+ln((number+of+days+since+2009+Jan+09)%2Fdays)+-+17.9183761889864))

I sketched a hand (inaccurately) drawn update of the green price line (did not update the regression):

https://bitcointalk.org/index.php?topic=2550946.0

In this OP I will always post the last updated chart:

Update 2017-01-03:
https://s3.postimg.org/kmzui60kj/logarithmic_03_01_2017.jpg
Donations: bitcoin:1Fe6B3Zo4HxaCD8ybi9A8zBRH2wKpciUxe

Calculate today's trendline value HERE (http://www.wolframalpha.com/input/?i=10^(2.66167155005961++*+ln((number+of+days+since+2009+Jan+09)%2Fdays)+-+17.9183761889864))

to the people saying it is quite impressive and such.
According to the graph, the price of one bitcoin would be around $ 4000 not $ 16000.

Why are you picking on the chart? It is simply a chart based on the past. It is very apolitical in that sense. Yes the expected price is far from the current price but we all know even by bitcoin standard there is massive pumping going on so we may soon be much closer to the expected value. And the spread info gives the reader some feeling of how far up or down the price might be from a middle path. Leave the chart in peace.

The thing is, when the actual graph is jumping all over the place, up and down, it's inevitable that it will intersect a smooth red line a few times. Every time it happens, you can call it amazing, but... you know...

Is there an altcoin version. Will like to do a comparative analysis to see if FUD and FOMO have quantitative measures on the market assays.

Some fantasies about the future ;D :

https://s9.postimg.org/rl7bkqa3z/kr_DJEnf_Ej_ZLk2p_1.jpg

https://s9.postimg.org/rl7bkqa3z/kr_DJEnf_Ej_ZLk2p_1.jpg

Some fantasies about the future ;D :

https://s9.postimg.org/rl7bkqa3z/kr_DJEnf_Ej_ZLk2p_1.jpg

https://s9.postimg.org/rl7bkqa3z/kr_DJEnf_Ej_ZLk2p_1.jpg

Some fantasies about the future ;D :

https://s9.postimg.org/rl7bkqa3z/kr_DJEnf_Ej_ZLk2p_1.jpg

https://s9.postimg.org/rl7bkqa3z/kr_DJEnf_Ej_ZLk2p_1.jpg

You actually think we'll still be at 10k in 2021? Doubtful.

where is the new army of greater fools ?

They are still studying in the school  ::) ;D

Lol if this would be real anyone owning 1 bitcoin is a millionaire in 10 years time

It's 2018, not 2017  ;D

Funny thing is that these predictions are working until they don't.
When environment is changing so will behavior of BTC. Old predictions then will be invalid.

This is also grossly how I see it.   Except that the arcs become wider and wider (longer and longer periods of down between the bubbles).  And look, we're heading for the next few years towards something like $3000, and the next bubble is maybe 5 or 6 years away.  The first one of size was in the summer of 2011.  The second one was at the end of 2013 (so 2-3 years).  The third one was at the end of 2017 (so 4 years).  This is why I think we're in for a bear period of a few years, down to a few $1000.  In 2014/2015, we went down a factor of 6.  In 2012, we went down a factor of about 10.  And then of course, there may be a last bubble.  Hard to say.  Once everyone has been burned once, where is the new army of greater fools ?

Amazing @anonymint's analysis:
https://steemit.com/trading/@anonymint/bitcoin-to-usd15k-in-march-usd8-5k-by-june-then-usd30-k-by-q1-2019 (https://steemit.com/trading/@anonymint/bitcoin-to-usd15k-in-march-usd8-5k-by-june-then-usd30-k-by-q1-2019)

1) Chart updated:

https://postimg.org/image/dmr2xq5np/

https://s18.postimg.org/66rtbxhyf/btcusd-09mar2018-3.jpg

==

Additional Information:

2) BTC/USD chart

https://postimg.org/image/9vcwy4kqd/

https://s18.postimg.org/eu0fcnojd/btcusd-wisdom09mar2018.jpg

---

3) S&P 500 chart

https://postimg.org/image/a84b4d0g5/

https://s18.postimg.org/eu0fcplzd/sp500usd-09mar2018.jpg

---

4) Fear Index

http://money.cnn.com/data/fear-and-greed/

https://postimg.org/image/dqgb0ogqt/

https://s18.postimg.org/fi99vl03t/MAj_Qw8_H4boq_M2e_1.jpg

---

5) Buffet sits in cash! ))

http://www.newsweek.com/warren-buffet-says-berkshire-hathaway-has-unique-problem-too-much-cash-819062

https://postimg.org/image/ddowueyg5/

https://s18.postimg.org/6zztr5tk9/z_ANJLqf_BMy_Wq_A9_1.jpg

===

All can I see - Big Short is coming  8) ::)

Additional Information:

2) BTC/USD chart

https://postimg.org/image/9vcwy4kqd/

https://s18.postimg.org/eu0fcnojd/btcusd-wisdom09mar2018.jpg

---

linear scale = bullshit

Amazing @anonymint's analysis:
https://steemit.com/trading/@anonymint/bitcoin-to-usd15k-in-march-usd8-5k-by-june-then-usd30-k-by-q1-2019 (https://steemit.com/trading/@anonymint/bitcoin-to-usd15k-in-march-usd8-5k-by-june-then-usd30-k-by-q1-2019)

discussed here:
https://bitcointalk.org/index.php?topic=3057203 (https://bitcointalk.org/index.php?topic=3057203)

Could u update Trolololo?  8)

Could u update Trolololo?  8)

Interestingly, the forecast almost falls in line with what McAfee has said.


https://ibb.co/i7BWo7

Has McAfee undergone that operation yet to remove his private parts that he made a bet on?  ::)

The Moon Math log projection isn't that far off from Trolololo's: https://www.moonmath.win/

Over the three bubbles, you see how the peak shifts down in the color range? The following bottoms also has shifted down in color.
I, a noob, was caught out during the latest bubble, expecting it to reach the previous peak color!
Is it possible to make a chart where the peaks & bottoms have the same color?

So... what's the current status of this rainbow? ;D

does anyone here know how to calculate Trololo's equation?

Where is Trolololo  ::) :o

Hello! I am writing to this forum for the first time. I was very interested in the work of Trolololo and I decided to get into it in detail. I carefully and thoroughly studied this whole forum https://bitcointalk.org/index.php?topic=831547.0 and made sure that its formulas in the past gave accurate results! Thank you very much Trolololo for your fundamental work.
       But I do not understand everything, so I am forced to turn to all of you and, above all, to the distinguished Trolololo for help and clarification ....
       Trolololo several times laid out similar, but slightly different formulas. All these formulas give different results and all these results change every day ... Today, 07/20/2019, the formulas give the following results:

10/22/2014 5-17-47
10 ^ (2.66167155005961 * ln ((number of days since 2009 Jan 09) / days) - 17.9183761889864) 11266
https://www.wolframalpha.com/input/?i=10%5E2.66167155005961++*+ln ((number+of+days+s+2009+Jan+09)%2Fdays)+-+17.9183761889864)

 
12/30/2014
10 ^ (2.9065 * ln ((number of days since 2009 Jan 09) / days) - 19.493)
31480
https://www.wolframalpha.com/input/?i=10%5E(2.9065++*+ln((nnumber+of+days+since+2009+Jan+09)%2Fdays)+-+19.493)

 
3/9/2015
10 ^ (3.1737 * ln ((number of days since 2009 Jan 09) / days) - 21.424)
59234
https://www.wolframalpha.com/input/?i=10%5E(3.1737++*+ln((nnew+of+days+since+2009+Jan+09)%2Fdays)+-+21.424)

 
05.28.2015
10 ^ (3.11800081827247 * ln ((number of days since 2009 Jan 09) / days) - 21.0858000278001)
44773
https://www.wolframalpha.com/input/?i=10%5E (3.1800081827247++*+ln ((number+of+days+s++2009+Jan+09)%2Fdays)+++21.0858000278001)

 
04/14/2016
10 ^ (2.84737734739566 * ln ((number of days since 2009 Jan 09) / days) - 19.2400124152881)
18323
https://www.wolframalpha.com/input/?i=10%5E2.84737734739566++*+ln ((number+of+days+s+2009+Jan+09)%2Fdays)+-+19.2400124152881)


01/10/2017
10 ^ (2.66167155005961 * ln ((number of days since 2009 Jan 09) / days) - 17.9183761889864)
11266
https://www.wolframalpha.com/input/?i=10%5E2.66167155005961++*+ln ((number+of+days+s+2009+Jan+09)%2Fdays)+-+17.9183761889864)

  

          In this regard, I have the following questions:
1) I would like to draw your attention to the fact that the first and last formulas on October 22, 2014, 17–47 and 01/10/2017 are absolutely identical !!! Why? Why, then, were changes made to the formula for three years?
 2) Which of these formulas is relevant today?
3) If I understand correctly, these formulas show the predicted price of Bitcoin after some time in the future. After what about time Bitcoin should reach the price, which shows the formula at the moment.
4) What are the days of brackets (number of days since 2009 Jan 09) / days) does this formula substitute for getting the correct result?

1) That was a typo. I updated all data in the chart, except I forgot to update the formula parameters in the chart... Updating the chart was a hard manual process, and so subject to minor errors.
2) The chart should be updated regularly...
3) I made those charts to have an idea of whether the BTC price was overvalued or undervalued at the moment of every update. The chart could also be useful for estimating under-over valuation for one or two years in the future. And also gave and idea of the enormous revalorization of BTC that was left by them. But I never did that as a prediction, because no one can predict the market behavior. The price hitting 10k with just days of difference... is just luck. No cristal ball here... Seriously.
4) The wolframalpha gave an approximation of the value at a given date, given that updating the chart was a hard process.

Glad to see the legendary Trolololo!!

Have you ever added overbought and oversold bands to better visualize those levels? Is there a model that includes bands that you like more?

It would be interesting to see where the overbought band is right now or 6 months ahead.

Rainbow chart looking great as always. As expected, Bitcoin will continue to move lower and lower in the rainbow as time passes, because there is only so much money in the world that will go into a single asset, so slowdown will occur, and as proof you can just look at the 2011, 2013, and 2017 peaks to see the lower progression. I think the light orange band (5th from top) is probably as high as Bitcoin will make it from this point on.

Bitcoin should recover into the green during the second half of this year, probably roughly follow that up for a bit next year and start poking into the yellow. Maybe 2025 post-halving we'll get a pump into the orange briefly. $400k range in 2025.

Love the rainbow. This was the first chart when I got back into bitcoin in 2017 that made me realize the growth potential for the future.

Do you (or anyone else) have a link to which ever rainbow chart (or the infamous one) you are referring to, and perhaps I (and others / and the students of the class) might be able to follow along with the visuals a wee bit moar better.

Hey I was wondering if you could update the bitcoin regression equation? It looks like you said in 2021 it's updated regularly but I'm seeing that the last update was in 2017.

If you click on the link within hotpassion's post (https://bitcointalk.org/index.php?topic=831547.msg57578569#msg57578569) - two post above yours, then you will see that the update of the graph goes all the way to today's date.

If you click on the link within hotpassion's post (https://bitcointalk.org/index.php?topic=831547.msg57578569#msg57578569) - two post above yours, then you will see that the update of the graph goes all the way to today's date.

P.S. I dunno how do you guys paste pictures here so they are displayed

Bump again! MoonMath.win is down! All we got is this: https://www.blockchaincenter.net/en/bitcoin-rainbow-chart/

I reference this as the LookIntoBitcoin version looks more relevant, as factors in the March 2020 low more accurately, as seems to have been adjusted to include it.

You should always remember what is written on one of the referenced web pages: "The color bands follow a logarithmic regression (introduced by Bitcointalk User trolololo in 2014), but are otherwise completely arbitrary and without any scientific basis."

Clearly it's not arbitrary when LookIntoBitcoin have modified the logarithmic curve, and haven't referenced the fact it's arbitrary or lacks any scientific basis. Probably because it's a mathematical based curve, nothing to do with science. The irony being that a logarithmic curve in itself isn't arbitrary, it's simply how you style it (connect the dots), even if the original remains arbitrary and unchanged.

You didn't get me. The Log curve is an approximation of price history (logarithmic regression). That is the scientific part.  But the rainbow is made by duplicating that curve parallel to itself with certain intervals that are not somehow "scientifically" linked to volatility, ATHs ant Lows.

And it does not look like they have modified the curve either. Here is my view of the trend as for now https://i.ibb.co/q9MmZx3/BTC-Plan-17.png

Like I said, just change the file extension to jpg (the server already has it) and put it inside the img brackets and it will show the image:

You didn't get me. The Log curve is an approximation of price history (logarithmic regression). That is the scientific part.  But the rainbow is made by duplicating that curve parallel to itself with certain intervals that are not somehow "scientifically" linked to volatility, ATHs ant Lows.

And it does not look like they have modified the curve either. Here is my view of the trend as for now
https://i.ibb.co/q9MmZx3/BTC-Plan-17.jpg

The first example of a logarithmic regression curve for Bitcoin was created by Bitcoin Talk user trolololo. This is the original chart [chart below], which shows how $BTC price could potentially evolve over time using log growth regression analysis:

@dragonvslinux

(...) the curve should be updated after adding new historical data to it (...)

There's actually two slightly differing models here, if not more online by now, not just the blockchain center version of the chart.

1. https://www.blockchaincenter.net/en/bitcoin-rainbow-chart/
2. https://www.lookintobitcoin.com/charts/bitcoin-rainbow-chart/

That is correct.

Useful video on YouTube called "The Bitcoin Power Law Growth Corridor" by Chad Thackray. Well worth watching.

The description says: We implement a model popularised by Harold Burger, which uses a log-log chart of bitcoin and then applies linear regression to establish a long term corridor of price action, which has worked well over the past 10 years. It's a useful indicator to zoom out and see the big picture, without getting worked up over day to day price action.

https://www.youtube.com/watch?v=wfi-bst4hmA (https://www.youtube.com/watch?v=wfi-bst4hmA)

Hello! I am writing to this forum for the first time. I was very interested in the work of Trolololo and I decided to get into it in detail. I carefully and thoroughly studied this whole forum https://bitcointalk.org/index.php?topic=831547.0 and made sure that its formulas in the past gave accurate results! Thank you very much Trolololo for your fundamental work.
       But I do not understand everything, so I am forced to turn to all of you and, above all, to the distinguished Trolololo for help and clarification ....
       Trolololo several times laid out similar, but slightly different formulas. All these formulas give different results and all these results change every day ... Today, 07/20/2019, the formulas give the following results:

10/22/2014 5-17-47
10 ^ (2.66167155005961 * ln ((number of days since 2009 Jan 09) / days) - 17.9183761889864) 11266
https://www.wolframalpha.com/input/?i=10%5E2.66167155005961++*+ln ((number+of+days+s+2009+Jan+09)%2Fdays)+-+17.9183761889864)

 
12/30/2014
10 ^ (2.9065 * ln ((number of days since 2009 Jan 09) / days) - 19.493)
31480
https://www.wolframalpha.com/input/?i=10%5E(2.9065++*+ln((nnumber+of+days+since+2009+Jan+09)%2Fdays)+-+19.493)

 
3/9/2015
10 ^ (3.1737 * ln ((number of days since 2009 Jan 09) / days) - 21.424)
59234
https://www.wolframalpha.com/input/?i=10%5E(3.1737++*+ln((nnew+of+days+since+2009+Jan+09)%2Fdays)+-+21.424)

 
05.28.2015
10 ^ (3.11800081827247 * ln ((number of days since 2009 Jan 09) / days) - 21.0858000278001)
44773
https://www.wolframalpha.com/input/?i=10%5E (3.1800081827247++*+ln ((number+of+days+s++2009+Jan+09)%2Fdays)+++21.0858000278001)

 
04/14/2016
10 ^ (2.84737734739566 * ln ((number of days since 2009 Jan 09) / days) - 19.2400124152881)
18323
https://www.wolframalpha.com/input/?i=10%5E2.84737734739566++*+ln ((number+of+days+s+2009+Jan+09)%2Fdays)+-+19.2400124152881)


01/10/2017
10 ^ (2.66167155005961 * ln ((number of days since 2009 Jan 09) / days) - 17.9183761889864)
11266
https://www.wolframalpha.com/input/?i=10%5E2.66167155005961++*+ln ((number+of+days+s+2009+Jan+09)%2Fdays)+-+17.9183761889864)

  

          In this regard, I have the following questions:
1) I would like to draw your attention to the fact that the first and last formulas on October 22, 2014, 17–47 and 01/10/2017 are absolutely identical !!! Why? Why, then, were changes made to the formula for three years?
 2) Which of these formulas is relevant today?
3) If I understand correctly, these formulas show the predicted price of Bitcoin after some time in the future. After what about time Bitcoin should reach the price, which shows the formula at the moment.
4) What are the days of brackets (number of days since 2009 Jan 09) / days) does this formula substitute for getting the correct result?

....

Hi Sergii,
It turns the model of Trolololo is nothing else than a power law. He wrote the formula, log10(Price)=A*ln(days)-C but this can be rewritten as Price=10^(A*ln(days)-C) or Price=days^(Aln(10))/10^C or price=B*days^n where B=1/10^C and n=A*ln(10).
It is a big deal because a power law first of all looks like a straight line in a log log graph and BTC looks exactly like that. .....