Exponential Grid [Phi, Pi, Euler]If you disagree with one of the EMH principles that price is too random, then by definition you must agree that historic price has deterministic function to a scenario ahead.
I personally believe that constants like phi, pi and e can mimic exponential growth of the price.
In this script, first grid is based on the Lowest price multiplied with self fraction of the constant.
For example:
If you are familiar with fib ratio 1.272, then you must know that it is 1.618 to the power of 0.5.
With default settings of exponent step 0.25
First grid = Lowest price x phi^0.25
Second grid = Lowest price x phi^0.25x2
Third grid = Lowest price x phi^0.25x3 and so on
The script will automatically find the lowest price and update the grid values.
Or you can set up your custom Lowest price manually if you feel like the All Time Low level loses its relevance value after long period.
There are 64 grids including Lowest price level. And it wasn't by a chance. Pine Script has a limitation of max 64 plots. Number of grids shown in the chart depends on the highest price. Once price breaks above ATH a couple of next grids will be plotted automatically. In most cases if everything is plotted, the chart appears squeezed and you'll need to zoom in to see it. Therefore, I adjusted it relatively to the scale of the chart for the comfort.
In some cases 64 plots aren't enough to cover the whole chart. For example, let's take a look at NVIDIA chart:
Since the price has started with 0.0333, it is way too small to cover all with default settings.
We are left with 2 choices:
Either Enable "Round"
OR increase Exponent Step (from 0.25 to 0.5 in the particular example below)
If you set constant to pi or e which is a bigger number than phi, expect the gaps to be bigger. To reduce it to a more gradual way of expansion you can decrease Exponent Step.
Constant
[HELPER] Math Constant Helper█ OVERVIEW
This indicator is to show constant in table using built-in math name space, coded in latest Pine Script version 5.
█ CREDITS
Credits to PineCoders.
█ FEATURES
- Display table by changing table position, font size and color.
MathConstantsLibrary "MathConstants"
Mathematical Constants
E() The number e
Log2E() The number log (e)
Log10E() The number log (e)
Ln2() The number log (2)
Ln10() The number log (10)
LnPi() The number log (pi)
Ln2PiOver2() The number log (2*pi)/2
InvE() The number 1/e
SqrtE() The number sqrt(e)
Sqrt2() The number sqrt(2)
Sqrt3() The number sqrt(3)
Sqrt1Over2() The number sqrt(1/2) = 1/sqrt(2) = sqrt(2)/2
HalfSqrt3() The number sqrt(3)/2
Pi() The number pi
Pi2() The number pi*2
PiOver2() The number pi/2
Pi3Over2() The number pi*3/2
PiOver4() The number pi/4
SqrtPi() The number sqrt(pi)
Sqrt2Pi() The number sqrt(2pi)
SqrtPiOver2() The number sqrt(pi/2)
Sqrt2PiE() The number sqrt(2*pi*e)
LogSqrt2Pi() The number log(sqrt(2*pi))
LogSqrt2PiE() The number log(sqrt(2*pi*e))
LogTwoSqrtEOverPi() The number log(2 * sqrt(e / pi))
InvPi() The number 1/pi
TwoInvPi() The number 2/pi
InvSqrtPi() The number 1/sqrt(pi)
InvSqrt2Pi() The number 1/sqrt(2pi)
TwoInvSqrtPi() The number 2/sqrt(pi)
TwoSqrtEOverPi() The number 2 * sqrt(e / pi)
Degree() The number (pi)/180 - factor to convert from Degree (deg) to Radians (rad).
Grad() The number (pi)/200 - factor to convert from NewGrad (grad) to Radians (rad).
PowerDecibel() The number ln(10)/20 - factor to convert from Power Decibel (dB) to Neper (Np). Use this version when the Decibel represent a power gain but the compared values are not powers (e.g. amplitude, current, voltage).
NeutralDecibel() The number ln(10)/10 - factor to convert from Neutral Decibel (dB) to Neper (Np). Use this version when either both or neither of the Decibel and the compared values represent powers.
Catalan() The Catalan constant
Sum(k=0 -> inf){ (-1)^k/(2*k + 1)2 }
EulerMascheroni() The Euler-Mascheroni constant
lim(n -> inf){ Sum(k=1 -> n) { 1/k - log(n) } }
GoldenRatio() The number (1+sqrt(5))/2, also known as the golden ratio
Glaisher() The Glaisher constant
e^(1/12 - Zeta(-1))
Khinchin() The Khinchin constant
prod(k=1 -> inf){1+1/(k*(k+2))^log(k,2)}
Euler Cubes - CubᵋI give you the "Euler Cubes", inspired by the mathematical number 'e' (Euler's number).
It is suggested (fibonacci ratios analogy) that price/e ratio can give Support/Resistance area's.
The first cube is made by a low/high of choice, for example:
You set the 'source low'/'source high' in position:
Then you choose the 'e ratio' (x times 'e')
This multiplies the distance 'high-low' times '0.271828' times 'the set number' .
For example, choosing 5 gives 5 x 0.271828 = 1.35914, the distance 'high-low' hereby multiplied by 1.35914, the following cubes multiply the previous distance by 1.35914.
(Settings below 5 will give cubes smaller than the 'high-low' distance)
In the case of x times 'e' = 5:
You can extend the lines:
Now you can give it an angle:
Do mind, using it over very little bars and using an angle can cause some lines to not align as intended, because for now, it is not possible to plot in between bars.
There are also 'Euler' SMA and EMA available with following length's:
27, 54, 82,109, 136, 163, 190 and 217
Cheers!
Return Error With Reference & Constant Value Enforcer FunctionsI found MichelT 's work thanks to LucF . One of its cool concepts that touched me was his error's function. Whenever something unexpected takes place, it returns an error's message right on the chart, one nobody can't say they can't see lol. I told him it would be cool if we could get specific messages related to specific cases, he said "there is a task for such feature". On the meantime I wanted to enrich his feature by making the function printing any number the user wants.
Another really cool thing I have been in love with are "Pine Coding Conventions", I can't express enough how thankful I am to the amazing team behind it. Just recently they introduced me to a new rule, one seeming very popular across the board, using all capital letters to define a constant value.
On this script I combined both error's printing message with a constant check functions that enforce the value must remain unchanged ever. I hope you like this work, I really enjoy seeing brilliant people coming up with some awesome ideas. Let's together make "Pine" a more cooler language.
