The speed-curvature power law of movements: a reappraisal

Myrka Zago, Adam Matic, Tamar Flash, Alex Gomez-Marin, Francesco Lacquaniti

Research output: Contribution to journalArticlepeer-review


Several types of curvilinear movements obey approximately the so called 2/3 power law, according to which the angular speed varies proportionally to the 2/3 power of the curvature. The origin of the law is debated but it is generally thought to depend on physiological mechanisms. However, a recent paper (Marken and Shaffer, Exp Brain Res 88:685–690, 2017) claims that this power law is simply a statistical artifact, being a mathematical consequence of the way speed and curvature are calculated. Here we reject this hypothesis by showing that the speed-curvature power law of biological movements is non-trivial. First, we confirm that the power exponent varies with the shape of human drawing movements and with environmental factors. Second, we report experimental data from Drosophila larvae demonstrating that the power law does not depend on how curvature is calculated. Third, we prove that the law can be violated by means of several mathematical and physical examples. Finally, we discuss biological constraints that may underlie speed-curvature power laws discovered in empirical studies.

Original languageEnglish
Pages (from-to)69-82
Number of pages14
JournalExperimental Brain Research
Issue number1
Publication statusE-pub ahead of print - Oct 25 2017


  • Drawing
  • Motor control
  • Statistical analysis
  • Two-thirds power law

ASJC Scopus subject areas

  • Neuroscience(all)


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