4.50 Measuring Fractal Dimension Directly from Price
Fractal dimension measures choppiness as a number: count price range over interval at two scales. D near 1 is a clean trend, D near 2 is chop, and H = 2 - D hands you the Hurst reading.
Independent research on systematic & quantitative trading
Aligrithm is an independent research publication on systematic trading, quantitative research, market microstructure, and adaptive systems. Long-form essays, code notebooks, and architecture breakdowns across eight pillars, built for traders who care more about how markets behave than about hype.
More about the publication →The ten pillars
Read in order. Each pillar walks you out of one trap with one new ability. The newest article is the worst place to begin.
- 1 The Scientific Trader Rebuild what you accept as evidence. Every rule becomes a hypothesis, every backtest an experiment you can falsify. 26
- 2 Indicator Engineering The input decides the ceiling. Build features with measurable properties that survive the tests. 82
- 3 Robust Systems Lab A strategy is not robust for surviving one friendly backtest. Here it survives hostile testing. 37
- 4 Market Structure Notes The same rule is edge on one instrument and noise on another. Read a market's personality before you deploy. 70
- 5 Microstructure Alpha The order-book layer. The same signal is worthless as taker flow and valuable as a maker improvement. 45
- 6 Portfolio Construction & System Death A real signal still loses if the size and correlations are wrong. Sizing is part of the signal. 47
- 7 Python Research Notebooks Stop taking results on faith. Re-run every claim on your own data and see whether it holds. 3
- 8 Physics, Geometry & Event-Driven Markets The frontier. Markets as event-driven nonlinear systems, not fixed-time price series. Read it last. 8
- 9 Prediction Market Arbitrage The cleanest money on Polymarket and Kalshi comes from prices that contradict each other, not prices that turn out wrong. 33
- 10 Cross-Sectional & Factor Investing Stop timing one asset. Rank the whole cross-section and let relative value, not direction, carry the return. 15
Latest articles
4.49 The Hurst Exponent from Fractal Dimension
The Hurst exponent reads the same persistence axis as the efficiency ratio, linked by H = 1 - alpha/2 and H = 2 - D. But it's estimated, not computed, and drifts with data length, so read it as a profile.
2.74 Legendre-Polynomial Trend and Trend Relative to Local Variation
Most indicators tell you which way price went. Fit a line to the window with Legendre polynomials and divide the slope by the within-window scatter, and you get a t-statistic for trend: direction plus how much to trust it.
4.57 Currency Personality and Correlation Blocs
Currencies cluster into blocs by their drivers: a European cluster anchored to EURUSD, a commodity cluster wired to specific exports, and a yield axis splitting havens from risk currencies. Trade several members of one bloc and you load one factor, not five bets.
2.60 The Ehlers Modified Hilbert Transformer
Pair price with its quarter-cycle shift to read instantaneous amplitude and phase. The textbook Hilbert transformer lags forever; the modified version is accurate only across the cycle band, which is the band you trade.
2.59 Convolution: Detecting Reversals by Folding Price
A market turn is a reflection in time, so fold price about a candidate bar and correlate the halves. A bright, scale-persistent symmetry stripe marks the reversal, at the cost of honest, unavoidable confirmation lag.
8.7 Mutual Information as a Regime / Noise Filter
Mutual information measures whether the next move is connected to the last few or just noise. Volatility can't see the difference; MI gates your system on when structure is present and off when it drains away.
2.58 The Even Better Sine Wave: Advancing Phase to Predict
Convert the swing to a clean sine wave, then advance its phase to read the cycle a few bars early. Genuine prediction, valid only in cycle mode; in a trend it fires confident false reversals, so gate it hard.
8.6 Entropy as a Market Choppiness Gauge
Chop price into up/down "words", histogram them, and measure their entropy: near 1 the market is choppy noise, near 0 it keeps rhyming. Same formula as the indicator-quality score, opposite meaning.
2.57 Adaptive Indicators: Tuning RSI to the Measured Cycle
Stop hardcoding RSI(14). Set the lookback to half the measured dominant cycle, feed it a band-pass input, and recompute every bar. Tuned to a persistent cycle it can even lead, but only in cycle mode.
4.54 Order Statistics Across Markets: Median and Range as Breadth
Compute one indicator across a universe and summarize the cloud with order statistics: median is the market state, median over IQR is a non-parametric breadth z-score. Outlier-proof regime weather, not a trigger.
2.56 Reading Reversals from Autocorrelation
At a real reversal the autocorrelation flips at every lag at once, not just one. Sum the bar-to-bar changes across all lags and the spike flags the turn, no cycle period required.