Psychological levels (Bank levels) PsychoLevels v2 - Tartigradia

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Psychological levels (Bank levels) plots "round" price levels above and below current price, by truncating after the nth leftmost digits, based on neuroscience research of how humans intuitively calculate in logarithms.
Psychological levels, also called bank levels, are "round" price numbers around which price often experience resistance or support, because traders and investors tend to set orders around these round numbers.
Calculation here is fully automatic and dynamic, contrary to other similar scripts, this one uses a mathematical calculation that extracts the 1, 2 or 3 leftmost digits and calculate the previous and next level by incrementing/decrementing these digits. This means it works for any symbol under any price range.

This approach is based on neuroscience research, which found that human brains intuitively approximate numbers on a logarithmic scale, adults and children alike, and similarly to macaques, for more info see Numerical Cognition, Weber-Fechner Law, Zipf law.

For example, if price is at 0.0421, the next major price level is 0.05 and medium one is 0.043. For another asset currently priced at 19354, the next and previous major price levels are 20000 and 10000 respectively, and the next/previous medium levels are 20000 and 19000, and the next/previous weak levels are 19400 and 19300.

* By default, strong upper level is in green, strong lower level is in red, medium upper level is in blue, medium lower level is in yellow, and weak levels aren't displayed but can be. Half levels are also displayed, in a darker color. Strong levels are increments of the first leftmost digit (eg, 10000 to 20000), medium levels are increments of the second leftmost digit (eg, 19000 to 20000), and weak levels of the third leftmost digit (eg, 19100 to 19200). Instead of plotting all the psychological levels all at once as a grid, which makes the chart unintelligible, here the levels adapt dynamically around the current price, so that they show the upper/lower levels relatively to the current price.
* A simple moving average is implemented, so that "half-levels" are also displayed when relevant (eg, medium level can also display 19500 instead of only 19000 or 20000). This can be disabled by setting smoothing to 1.
* By default, the script runs on the daily timeframe , whatever the current chart's timeframe is. This is to reduce the variability in levels, to make it less noisy than intraday price movement, but this can be changed in the settings.
* The step can be adjusted to increase the gap between levels, eg, if you want to display one every 2 levels then input step = 2 (eg, 22000, 24000, 26000, etc), or if you want to display quarter levels, input 0.25 (eg, 22000, 22250, 22500, etc). The default values should fit most use cases and cover most psychological levels.

I made this script mainly to train with PineScript, but I found it surprisingly accurate to define levels that are respected by price movements. So I guess it can be useful for new traders and experienced traders alike, as it's easy to forget that psychological levels can often be as strong if not stronger than technical levels. It can also be used to quickly screen other minor assets for trading opportunities. For example, a hybrid strategy would be to manually define levels on BTCUSD but using this script to automatically define levels in crypto altcoins and quickly screen them for a trade opportunity that can be greater than with BTCUSD but with the same trend.

Changes compared to v1:
* Deduplicated redundant calculations and hence faster script.
* Added half-step levels, which allows to more easily see breakouts (because the levels are still on-screen).
* All steps are now configuration on the GUI.
* Revamped color scheme.
* And major reasons to post as a separate v2 script rather than updating: because we can't update the original description nor screenshot. I have now read more about the House Rules and saw other scriptmakers, so I am trying to write better descriptions like wizards do, by explaining not only how the script works but what the underlying financial concept is to a neophyte audience.
Release Notes: Clean up unused variables and typos in comments
Release Notes: A great tip: in practice, the number of consecutive dots on the same line influences the strength of the level: the longer the chain of dots, the more you can expect this price level to be significant. The length does not mean the level will necessarily hold, but that other traders are likely to monitor if it holds, and if not then price will break down. Hence, longer levels are good spots to place stop losses, or to enter trades depending on your strategy. In general, a single dot is not enough to consider a level significant, but 2 or more is a good enough level, and 10+ is a strong level. Intuitively, this makes sense, and is what pro traders do: the longer a level is tested, the stronger it is. This indicator can visually represent this intuition and allows to use it as a more systematic trading signal.
Release Notes: Please enable "Scale price chart only" in the chart's scale's options, as otherwise major levels may make the chart's scale very small and hard to read.
Release Notes: Update:
* Change default timeframe to Chart (so that it adapts to the user selected timeframe). But it is still advised to use the levels mostly on the daily or weekly timeframes.
Release Notes: Update:
* Disable SMA by default, so that levels are instantly reactive to price changes, and also levels make more sense now (before they could appear triangular, now levels are always a straight line, it eases finding patterns in price action).
Release Notes: Update:
* Tweak color palette a bit to be more visible.
Release Notes: Update chart.
Release Notes: Update:
* Tweak color palette to be more visible, again.
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