Visualizing Brownian motion with particle systems in blender
The development and continuous improvement of the microscope lead to many important discoveries. One of them was made by Robert Brown a botanist that described the movement of pollen particles immersed in water. Concerned that the movement could be life-related he repeated the experiment with inorganic matter and a movement pattern with the same characteristics was observed.
One of the ways Brownian motion can be described mathematically is as a stochastic process. Brownian motion can be easily modeled and extended to higher dimensions, as each dimension contains a one-dimensional Brownian motion component.
As Brownian motion involves the motion of small particles is a fitting theme to work with particle systems and force fields in blender. A particle system is a blender functionality used to emit lots of objects from a mesh, such object is often called emitter. While a force field offers a way to influence the simulation and add extra movement to the objects. In both cases, the effect f those functionalities can be observed in the complete animation. However, selected frames from the animation are accessible to create an image.
To define the force field we can use the output of the Brownian motion function to define a curve that maps through each of the points in the curve.
Then we add a force type force field, that will attract the particles in the particle system towards the curve and follow it. The force field strength is set to a negative number to attract the particles and the shape is set up as surface.
With the force field in place, we can start with the particle system. Thus we add a new object to the scene to be used as the emitter. Then the particles and the lifetime of the particles are increased so the particles can reach the end of the Brownian motion curve before the animation ends. And the gravity weight is reduced to zero, then the only force field that can interact with the system will be the one from the curve.
Then a new mesh is created, this will be used as a template for each particle in the particle system. As it’s going to be only a template can be placed anywhere in the scene.
Finally, a simple material can be added to the template cube so all the particles share the same material. As random numbers are used for this animation the result is unlikely to be the same for you, but here are some examples of renders at different frames.
Why do small particles move in that specific pattern is a question that continues to be researched. However, accurate measurements of particle displacement have shown that the particle dynamic behaves as a chaotic system. Furthermore mathematical analysis of Brownian motion shown strong dependence on the initial conditions of the dynamical system. A common property of dynamical systems that exhibit hard chaos. Although statistical properties of Brownian motion are well defined, improvements over the mathematical model of Brownian motion as well as the measurement techniques will lead to new clues and discoveries.
Know you have an example of how to use particle systems and force fields to make a visual representation of a physical phenomenon. Also a better understanding of Brownian motion and some discoveries regarding it. The complete code for this post can be found on my GitHub by clicking here. Talk to you soon.
Recommended reading
Brownian motion and microscopic chaos by Detlef Durr and Herbert Spohn
