Particle Physics Moving Average

This indicator simulates the physics of a particle attracted by a distance-dependent force towards the evolving value of the series it's applied to.

Its parameters include:
  • The mass of the particle
  • The exponent of the force function f=d^x
  • A "medium damping factor" (viscosity of the universe)
  • Compression/extension damping factors (for simulating spring-damping functions)

This implementation also adds a second set of all of these parameters, and tracks 16 particles evenly interpolated between the two sets.

It's a kind of Swiss Army Knife of Moving Average-type functions; For instance, because the position and velocity of the particle include a "historical knowlege" of the series, it turns out that the Exponential Moving Average function simply "falls out" of the algorithm in certain configurations; instead of being configured by defining a period of samples over which to calculate an Exponential Moving Average , in this derivation, it is tuned by changing the mass and/or medium damping parameters.

But the algorithm can do much more than simply replicate an EMA ... A particle acted on by a force that is a linear function of distance (force exponent=1) simulates the physics of a sprung-mass system, with a mass-dependent resonant frequency. By altering the particle mass and damping parameters, you can simulate something like an automobile suspension, letting your particle track a stock's price like a Cadillac or a Corvette (or both, including intermediates) depending on your setup. Particles will have a natural resonance with a frequency that depends on its mass... A higher mass particle (i.e. higher inertia) will resonate at a lower frequency than one with a lower mass (and of course, in this indicator, you can display particles that interpolate through a range of masses.)

The real beauty of this general-purpose algorithm is that the force function can be extended with other components, affecting the trajectory of the particle; For instance "volume" could be factored into the current distance-based force function, strengthening or weakening the impulse accordingly. (I'll probably provide updates to the script that incoroprate different ideas I come up with.)

As currently pictured above, the indicator is interpolating between a medium-damped EMA-like configuration (red) and a more extension-damped suspension-like configuration (blue).

This indicator is merely a tool that provides a space to explore such a simulation, to let you see how tweaking parameters affects the simulations. It doesn't provide buy or sell signals, although you might find that it could be adapted into an MACD-like signal generator... But you're on your own for that.
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