Technique · Simulations
Synchrony
A grid of coupled oscillators falling into step: marching patches, spreading phase waves and spinning vortices.
Synchrony is a simulation that evolves step by step. Every piece on Synapse Drip is made from a recipe that layers techniques like this one, and you can change any of it in the Studio.
Good to know
- The cells of the heart's natural pacemaker, the sinoatrial node, number only about ten thousand, and each beats at its own rate, but they pull each other into step and set the rhythm for the whole heart.
- A vortex in the phase, a point around which the phase turns through one full circle, cannot be undone by smooth changes; it can only be removed by meeting a vortex that turns the opposite way, so vortices come and go in pairs.
- Neurons, crickets chirping, applauding audiences and the generators of the electric grid all tend to fall into step in the same way, which is why this one model has been used so widely.
- Yoshiki Kuramoto wrote this model down in 1975; it explains how large crowds of oscillators fall into step, as the fireflies of Southeast Asia do when thousands of them flash in time on a riverbank.
- In 1665 Christiaan Huygens, lying ill in bed, noticed that two pendulum clocks hung on the same beam swung in opposite directions and in perfect time, the first recorded case of synchronisation.
The mathematics
- Each oscillator follows d(phase)/dt = w + 2.20 times the average of sin(neighbour phase - own phase) over its neighbours, where w is its own rate, drawn from a bell curve of width 0.32.
- If every oscillator were coupled to every other, the crowd would begin to fall into step once the coupling passed about 0.51, 1.6 times the width of the spread; with only near neighbours coupled, as here, the story is richer and patches and vortices appear instead.
- The picture blends the phases as little arrows, not as angles, so that a smooth turn through zero does not show as a seam; where neighbouring arrows disagree the colour dims, which marks the cores of the vortices.
In art
- Patterns with swirling points like this one appear in liquid-crystal films under crossed polarisers, in fingerprints and in the whorls of hair, wherever a direction field has to turn through a full circle.
- Synchrony is a theme of installation art: banks of metronomes, flashing lights and clapping machines, in which an audience watches order appear without a conductor.
More ways to use it
Related techniques
Reaction-diffusion · Cellular automata · Sandpile · Grain growth · Slime mould · Flocking boids · Attractor cloud · Elementary automaton