This tool is part of my research on the nature of the markets and understanding the relation between dimension and chaos theory.
To take full advantage of this indicator, you need to incorporate some principles and concepts:
- Traditional is linear and Euclidean, which makes very difficult its modeling.
- Linear techniques cannot quantify non-linear behavior
- Is it possible to measure accurately a wave or the surface of a mountain with a simple ruler?
- Fractals quantify what Euclidean Geometry can’t, they measure chaos, as they identify order in apparent randomness.
- Remember: Chaos is order disguised as randomness.
- Chaos is the study of unstable aperiodic behavior in deterministic non-linear dynamic systems
- Order and randomness can coexist, allowing predictability.
- There is a reason why Dimension was invented, we had no way of measuring fractal-based structures.
- Benoit Mandelbrot used to explain it by asking: How do we measure the coast of Great Britain?
- An easy way of getting the need of a dimension in between is looking at the Koch snowflake.
- Market prices tend to seek natural levels of ranges of balance. These levels can be described as attractors and are determinant.
Fractal Dimension Index ('FDI')
Determines the persistence or anti-persistence of a market.
- A persistent market follows a market trend. An anti-persistent market results in substantial around the trend (with a low r2), and is more vulnerable to price reversals
- An easy way to see this is to think that dimension measures what is in between mainstream dimensions. These are:
- One dimension: a line
- Two dimensions: a square
- Three dimensions: a cube.
--> This will hint you that at certain moment, if the market has a Dimension of 1.25 (which is low), the market is behaving more “line-like”, while if the market has a high Dimension, it could be interpreted as “square-like”.
- 'FDI' is trend agnostic, which means that doesn't consider trend. This makes it super useful as gives you clean information about the market without trying to include trend stuff.
Question: If we have a game where you must choose between two options.
1. a horizontal line
2. a vertical line.
Each iteration a Horizontal Line or a Square will appear as continuation of a figure. If it that iteration shows a square and you bet vertical you win, same as if it is horizontal and it is a line.
- Wouldn’t be useful to know that dimension is 1.8? This will hint square. In the markets you can use 'FD' to filter mean-reversal signals like , stochastics, Regular divergences, etc.
- Wouldn’t be useful to know that dimension is 1.2? This will hint Line. In the markets you can use 'FD' to confirm trend following strategies like Moving averages, , Hidden divergences.
dimension is obtained from the ‘hurst exponent’.
'FDI' = 2 - 'Hurst Exponent'
Musashi version of the Classic 'OG' Dimension Index ('FDI')
- By default, you get 3 fast 'FDI's (11,12,13) + 1 Slow 'FDI' (21), their interaction gives useful information.
- Fast 'FDI' cross will give you gray or red dots while Slow 'FDI' cross with the slowest of the fast 'FDI's will give white and orange dots. This are great to early spot trend beginnings or trend ends.
- A baseline (purple) is also provided, this is calculated using a 21 period with 1.618 'SD', once calculated, you just take midpoint, this is the 'TDI's (Traders Dynamic Index) way. The indicator will print purple dots when Slow 'FDI' and baseline crosses, I see them as Short-Term cycle changes.
- Negative slope 'FDI' means trending asset.
- Positive most of the times hints correction, but if it got overextended it might hint a rocket-shot.
- 'FDI' between 1.0≤ 'FDI' ≤1.4 will confirm trend following continuation signals.
- 'FDI' between 1.6≥ 'FDI' ≥2.0 will confirm reversal signals.
- 'FDI' == 1.5 hints a random unpredictable market.
- As you must know, fractals tend orbit certain spots, this are named Attractors, this happens with any behavior. The market of course also shows them, in form of , Supply Demand, etc. It’s obvious they are there, but now we understand that they’re not linear, as the market is , so simple trendline might not be the best tool to model this.
- I’ve noticed that when the Musashi version of the 'FDI' indicator start making a cluster of multicolor dots, this end up being an attractor, I tend to draw a as that area as price tend to come back (I still researching here).
Extra useful stuff
- Momentum / speed: Included by checking Study in the indicator properties. This will add two RSI’s (9 and a 7 periods) plus a baseline calculated same way as explained for 'FDI'. This gives accurate short-term trends. It also includes divergences (regular and hidden), deactivate with a simple check in the section of the properties.
- BBWP ( with Percentile): Efficient way of visualizing as the percentile of expansion. This line varies color from Iced blue when low and magma red when high. By default, comes with the High vols deactivated for better view of 'FDI' and while all studies are included. DDWP is trend agnostic, just like 'FDI', which make it very clean at providing information.
- Ultra Slow 'FDI': I noticed that while using BBWP and , the indicator gets overcrowded, so there is the possibility of adding only one 'FDI' + its baseline.
Final Note: I’ve shown you few ways of using this indicator, please backtest before using in real trading. As you know trading is more about risk and trade management than the strategy used. This still a work in progress, I really hope you find value out of it. I use it combination with a tool named “Musashi_Katana” (also found in TradingView).