# The relationship between speed and curvature differs in autistic and non-autistic tracing movements

## TL;DR

The study finds that autistic and non-autistic people move differently when drawing shapes, which could help explain how they perform complex tasks like writing.

## Contribution

The study reveals a novel difference in the speed-curvature relationship during tracing movements between autistic and non-autistic individuals.

## Key findings

- Autistic and non-autistic adults differ in their speed-curvature relationship during shape tracing.
- Non-autistic participants showed narrower speed oscillations, while autistic participants had broader modulation.
- These differences may reflect how movement signals are filtered in the body.

## Abstract

A growing field documents differences in autism in movement-based tasks such as handwriting, throwing a ball and social gestures. Usefully, complex movements such as social gestures and cursive handwriting can be decomposed to signature regularities that match those of “pure frequency” shapes including spirals, ellipses and rounded triangles. By studying the way that autistic and non-autistic people draw pure frequency shapes we can therefore predict movement patterns for a range of complex functional actions and gestures, and we can gain insights that may help us understand potential mechanisms underlying any differences. Correspondingly, we recorded the x and y position of a stylus tip as 21 autistic and 19 non-autistic adults (matched for age, IQ, and sex) traced a range of pure frequency shapes on a tablet. The relationship between speed and curvature across the pure frequency shapes typically follows a set of mathematical equations which can be thought of as a “spectrum of power laws”. We compared the speed-curvature relationship between groups and, additionally used fast Fourier transform (FFT) to investigate potential mechanisms. Autistic and non-autistic adults differed in the relationship between speed and curvature. FFT revealed that non-autistic participants narrowly modulated speed oscillations around target frequencies, while autistic participants showed broader speed modulation profiles, potentially indicative of differences in the bodily filtering of outgoing movement signals coming from the brain. Our results enable predictions about how autistic individuals might execute a range of functional movements, and may help in the development of support structures for complex tasks like writing.

The online version contains supplementary material available at 10.1038/s41598-026-37067-z.