🎉 New paper alert! 🧠 The velocity-curvature power law is one of the 'kinematic laws of nature' (Flash 2021), a 'fundamental law of human control' (Zago et al. 2016), and one of the 'kinematic regularities' (Frith & Frith 2023) thought to underlie all biological motion. 1/9.

📖 Full paper: 🎯 Hat tip to this MATLAB blog coverage: 🧰Psychtoolbox: #Psychtoolbox #VisionScience #ColourPerception #TerryPratchett.

From fictional octarine to real olo – whimsical fantasy becomes science fact, one precisely controlled experiment at a time. MATLAB with Psychtoolbox doing some serious psychophysics wizardry! 🧙‍♂️.

The Oz system (this time please do look behind the curtain!) uses precisely targeted lasers to stimulate only M-cones in your retina, bypassing the normal colour mixing your brain does.

While Pratchett's octarine was "a sort of greenish-purple," olo is described as blue-green with unprecedented saturation.

#MATLAB #MATLABambassador.James Fong and colleagues used Psychtoolbox (the MATLAB toolbox that I owe my job too!) to control their RGB projector during the colour matching experiments.

Terry Pratchett gave us octarine - the magical 8th colour of the spectrum, visible only to wizards and of course cats 🐱. UC Berkeley researchers have discovered "olo" - a real colour 🎨 that exists outside standard human vision… so far visible to only 5 people in the world! ✨.

Proper spectral estimation isn't just academic nicety - it's the difference between detecting real clinical population kinematic signatures vs chasing measurement artefacts 🏥✨.

That moment when you discover a paper that does exactly what you need, and MATLAB already has a battle-tested implementation pmtm() waiting in the toolbox. 🤯 Now we can confidently say we're 'making all the right noises' for biological motion simulation.

The journey fft() → pwelch() → pmtm() represents evolution from naive approaches, to widely adopted standards, to gold standard methods for power spectral density estimation 📈 Decades of signal processing wisdom, hopefully getting us closer to the truth.

Now imagine building synthetic data with incorrectly characterised noise - rather problematic! 🌪️ (Obviously not speaking from experience. 😅).

Get noise estimation wrong, and you'll mistake sensor jitter for genuine kinematic signatures ⚡. In Fraser et al. 2025 (, we showed that legacy protocols can generate spurious β≈1/3 due to noise and filtering artifacts.

Why obsess over this for movement research? Our velocity-curvature power law exponents β are exquisitely sensitive to background noise. If you're simulating biological trajectories, you need to verify what noise you actually added!.

pmtm() uses multiple orthogonal "windows" to peek at your data from different angles, then averages the results. It's like having a panel of experts, each seeing the data from a unique vantage point – resulting in massive variance reduction!.

Now we've switched to MATLAB's pmtm(). As McCoy et al. 1998 ( rather politely noted when introducing the method: the multitaper "produces much better results than using the periodogram". and it handles α=3 beautifully! 🎯.

But simulating biological motion might need extreme values (α=3 "black noise" which after diff() would be the alleged biological pink!) beyond MATLAB's built-in dsp.colorednoise range of [-2,2].

Following best practices from Wijnants et al. 2013 (, pwelch() works well for standard noise colours.

Enter MATLAB's pwelch() periodogram function - a proper upgrade! It cleverly chops your data into overlapping chunks and averages them. Like getting multiple opinions instead of trusting one dodgy measurement 📈 Much more civilised.

We talked about noise colour (purple, blue, white, pink, red, black, i.e. α [-2,-1,0,1,2,3] when 1/f^α) way back in October:

Started with fft() for quick and dirty noise colour estimation in our biological motion power law work. Alas more data doesn't make it more accurate 📊 Not ideal when chasing subtly divergent movement signatures in Parkinson's and Autism. #MATLAB #MATLABambassador.

RT @CRAE_IOE: Our October #CRAEwebinar:.Demystifying Emotion-Processing: Autism, Alexithymia & Psychological Mechanisms. @ConnorTKeating w….