KILLED · no edge
Hypothesis
The Higuchi/box-counting fractal dimension $D$ of a price window distinguishes smooth trends ($D\to1$) from rough chop ($D\to2$); regime-gating on $D$ improves a trend book.
Math — box-counting dimension
$$ D = \lim_{\epsilon\to 0}\frac{\log N(\epsilon)}{\log(1/\epsilon)} $$
Method
Higuchi FD on rolling 128-bar windows as a trend/chop gate, 30 symbols, costs applied.
Results
| Correlation of $D$ with realized vol | high (redundant) |
| Incremental edge over a vol filter | none |
Fractal dimension is, empirically, a repackaged volatility measure — it correlates ~0.9 with realized vol and adds nothing a simple ATR gate does not. Elegant, redundant. Killed.
Before adopting an exotic estimator, regress it on the boring one. If $D$ is 0.9-correlated with ATR, you have re-derived ATR with extra steps.