Are ranges the same at every timeframe? Six futures markets, eight timeframes.

A "range" here is the high-low span of the single candle whose close broke out of the previous range -- the same shape at 1 minute or at 4 hours. "Fractal" would mean the scale-free numbers (how often it continues, how many bars it survives) look the same no matter which timeframe you pick; the numbers that carry units (how wide the range is) should instead grow in a predictable power-law way with the timeframe. We measured both, on ES, NQ, YM, RTY, GC and CL, October 2018 through July 2026.

Probability map, not a directional call. what this means →

The scale-free numbers

Six metrics that carry no units -- a probability, a ratio, a share -- plotted against timeframe (log scale) for all six markets. If ranges are truly fractal, each line should be close to flat: the same number whether you're looking at a 1-minute range or a 4-hour range.

The power law

Median range width, normalized so each market's own 15-minute range equals 1, plotted log-log against timeframe. A straight line here means range width grows as timeframe to a fixed power (median_range = a x TF^H). The dashed reference line is what a pure random walk (Brownian motion) would produce, H = 0.5.

H = 0.5 is the random-walk benchmark: range width grows with the square root of time. An H consistently above 0.5 means range widens a little faster than a random walk would predict, at every timeframe measured.

By session (15-minute ranges)

The same 15-minute ranges, split by the ET session in which they formed (tagged by the hour the breakout bar opened). The 17:00-18:00 ET daily maintenance hour is excluded.

Honest reading

• Continuation odds (P(continue)) are modestly better than a coin flip at every timeframe measured (roughly 61-68% across 1 minute to 4 hours, all six markets) and stay in a fairly narrow band as timeframe grows -- this part of the claim holds up.
• Run structure is close to scale-free too: ranges-per-series (~3.5-4.0) and the share of single, non-continuing ranges (~31-38%) look almost the same at 1 minute as at 4 hours.
• Where it breaks: the share of ranges that break upward is NOT scale-free -- it drifts from about 51% at 1 minute to 54-58% at 4 hours across every market measured. Bigger bars capture more of each market's multi-year upward drift, so a 4-hour range is not just a scaled-up 1-minute range.
• The power-law exponent H sits between 0.53 and 0.59 across the six markets -- close to a random walk's 0.5, but consistently a little above it at every timeframe we measured.
• This is descriptive geometry, not a trading signal: no costs, no fills, no edge claim. The underlying series are spliced continuous contracts with no roll adjustment, which can add a handful of extra breakout events exactly at quarterly roll dates -- not corrected for here.

Range definition: 18:00 ET-anchored trading day, close-break rule (see /methodology). Window: 2018-10-01 through the end of available data (2026-07). Markets: ES, NQ, YM, RTY, GC, CL. Source: our own databento continuous-futures 15-second bars.