Comparison of Classical Kinematics, Entropy, and Fractal Properties As Measures of Complexity of the Motor System in Swimming
Authors: Tiago M. Barbosa, Wan X. Goh, Jorge E. Morais, Mário J. Costa, David Pendergast
DOI / Source: 10.3389/fpsyg.2016.01566
Date: 07 October 2016
Reading level: Intermediate
Why This Matters for Freedivers
Freediving performance is heavily technique-driven: small inefficiencies waste oxygen and add CO₂ for no benefit. This paper gives you a useful way to think about technique beyond “looks smooth”: it shows how movement can be measured as predictable vs. messy and simple vs. complex. Even if it’s about swimming strokes, the same idea applies to freediving finning—better technique often means less “speed wobble,” more repeatability, and lower energy cost.
Synopsis
When people talk about “good technique,” it often sounds subjective: “smooth,” “efficient,” “less splash.” This study tries to put numbers on that idea using three different lenses applied to swimming—one classic (traditional biomechanics) and two from the world of complexity science.
The researchers tested 68 high-level swimmers doing four all-out 25 m efforts—one for each stroke (front-crawl, backstroke, breaststroke, butterfly). They attached a speed sensor to the swimmer’s hip and recorded how speed changed moment to moment. From that speed-time signal, they calculated:
1) Speed fluctuation (dv) — a classic measure of how much your speed wobbles around your average speed within each stroke cycle. Big speed swings usually mean you’re repeatedly accelerating and decelerating, which costs extra energy because you must keep “re-buying” momentum while fighting drag.
2) Approximate entropy (ApEn) — a measure of how predictable or repeatable the speed pattern is. Lower values mean the pattern repeats in a more regular way; higher values mean it’s more irregular or “random.”
3) Fractal dimension (D) using Higuchi’s method — a measure of how complex or jagged the signal is across different time scales. Higher D generally means a more complex signal.
The results show that each stroke has its own “signature”: - Breaststroke had the largest speed fluctuation (biggest speed ups and slow downs), which fits what you see: strong propulsive bursts followed by more noticeable deceleration phases. - Front-crawl and backstroke had the lowest speed fluctuation, suggesting a steadier speed profile and, usually, better efficiency at a given pace. - For approximate entropy, front-crawl tended to be the most predictable (lowest ApEn), while backstroke showed higher irregularity (highest ApEn) in this dataset. - For fractal dimension, breaststroke came out as the most complex (highest D), with front-crawl/backstroke lower and butterfly in between.
Why should anyone outside competitive swimming care. Because these metrics give you a framework for understanding technique and efficiency: - If your movement causes large speed swings, you’re paying extra energy costs to re-accelerate your body and overcome drag repeatedly. - If your pattern is less repeatable (higher entropy), it can hint at coordination challenges, instability, or a technique that isn’t yet “automated.” - Complexity measures can sometimes detect meaningful changes that simple averages miss—useful when improvements are tiny but real.
For freedivers, the direct takeaway isn’t “train breaststroke.” It’s the principle: efficiency often looks like smoother speed, fewer unnecessary accelerations, and a more repeatable movement pattern. If you ever film dynamic apnea or open-water finning, you can use this mindset: aim for propulsion that is steady, rhythmic, and consistent, not “bursty.”
Abstract
The aim of this study was to compare the non-linear properties of the four competitive swim strokes. Sixty-eight swimmers performed a set of maximal 4 × 25 m using the four competitive swim strokes. The hip’s speed-data as a function of time was collected with a speedo-meter. The speed fluctuation (dv), approximate entropy (ApEn) and the fractal dimension by Higuchi’s method (D) were computed. Swimming data exhibited non-linear properties that were different among the four strokes (14.048 ≤ dv ≤ 39.722; 0.682 ≤ ApEn ≤ 1.025; 1.823 ≤ D ≤ 1.919). The ApEn showed the lowest value for front-crawl, followed by breaststroke, butterfly, and backstroke (P < 0.001). Fractal dimension and dv had the lowest values for front-crawl and backstroke, followed by butterfly and breaststroke (P < 0.001). It can be concluded that swimming data exhibits non-linear properties, which are different among the four competitive swimming strokes.