Magneto: An Exploration of Lorentz Force

June 28, 2011

Fields are an important concept to understand in generative design, they are the things that can control compositions and create natural pattern formation. In my work, either particles are interacting with each other and defining their movement or they movement is based on a field in the space where they are put, or both. The images in this post were generated by a real-time particle simulation of 5000 charged particles interacting with magnetic fields. This fundamental theory/law is used to derive their motion is based on the Lorentz Law in Fields and Waves. In physics Lorentz Force defines how a charged particle (point charge) is affected by an electromagnetic field. Lorentz Law states that the force on a changed particle or point charge is equal to the charge of the particle times the electric field which it is placed in, plus its charge times its velocity crossed with the magnetic field present. If there is more than one magnetic field, this equation can be solved for each magnetic field and summed to get the total resultant force. One thing to keep in mind is that these equations yield a vector force (i.e.. 3D), hence these are 3D renderings. These images were generated solely using the latter half of the equation that just uses the magnetic field (electrostatic field calculation are computational expensive and require more clever calculation and programming techniques to render in real-time…I’ll get to this later :). Its hard to see in these images, but I used the camera distance from the particle to calculate its opacity, this simulates fog and gives the images better depth.

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