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TASC 2010-06 | Fractal Dimension (Ehlers)


Traders' Tip text

While the WealthScript code that replicates the Fractal Dimension indicator (FDI) is given below, FDI will be added to Wealth-Lab’s TASCIndictors library for ease of use (see FractalDim). In the image it’s clear that when the FDI is rising the market tends to remain in a trading range, and conversely the market trends as the indicator falls.


Figure 1. The information provided by the Fractal Dimension Indicator is not unlike that of Welles Wilder’s ADX, albeit inverted.

WealthScript Code (C#)

using System;
using System.Collections.Generic;
using System.Text;
using System.Drawing;
using WealthLab;
using WealthLab.Indicators;

namespace WealthLab.Strategies { public class FractalDim : WealthScript { StrategyParameter _n; StrategyParameter _per;

public FractalDim() { _n = CreateParameter("N", 30, 10, 60, 2); // An even number _per = CreateParameter("Average Period", 20, 10, 55, 1); }

protected override void Execute() { HideVolume(); int N = _n.ValueInt; int avPer = _per.ValueInt; DataSeries avg = AveragePrice.Series(Bars); DataSeries smooth = FIR.Series(avg, "1,2,2,1"); DataSeries n3 = (Highest.Series(smooth, N) - Lowest.Series(smooth, N)) / N; int per = N / 2; DataSeries n1 = (Highest.Series(smooth, per) - Lowest.Series(smooth, per)) / per; DataSeries smooth_ = smooth >> per; DataSeries n2 = (Highest.Series(smooth_, per) - Lowest.Series(smooth_, per))/ per; DataSeries ratio = new DataSeries(Bars, "Fractal Ratio"); DataSeries dimen = new DataSeries(Bars, "Fractal Dimension"); double log2 = Math.Log(2); for (int bar = N; bar < Bars.Count; bar++) { if (n1[bar] > 0 && n2[bar] > 0 && n3[bar] > 0) ratio[bar] = 0.5 * ((Math.Log(n1[bar] + n2[bar]) - Math.Log(n3[bar])) / log2 + dimen[bar-1]); else ratio[bar] = ratio[bar-1]; if (bar < avPer) dimen[bar] = ratio[bar]; else dimen[bar] = SMA.Value(bar, ratio, avPer); } ChartPane fdPane = CreatePane(40, true, true); SetPaneMinMax(fdPane, 1.1, 1.7); DrawHorzLine(fdPane, 1.4, Color.Red, LineStyle.Solid, 1); DrawHorzLine(fdPane, 1.6, Color.Red, LineStyle.Solid, 1); PlotSeries(fdPane, dimen, Color.Blue, LineStyle.Solid, 2); } } }

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