######Renders Peter de Jong attractors for your entertainment!
A small project of mine, but I am proud of the results and they are actually interesting so I thought I'd put it here.
In dynamical systems, an attractor is a set of physical properties toward which a system tends to evolve, regardless of the starting conditions of the system.
An attractor is called strange if it has a fractal structure. This is often the case when the dynamics on it are chaotic, but strange nonchaotic attractors also exist.
(Wikipedia)
Specifically, the Peter de Jong attractor is an attractor defined by this system:
This system is quite chaotic, in that even a slight adjustment of the initial conditions or constants in the system (a, b, c, d) causes the system to manifest in a dramatically different way. To create animation, the renderer increments the constants by a small delta each frame to update the image, changing the trajectory of the system.
The visual representation of the attractor is a point cloud of many iterations of the system, a trace of the trajectory.
As the image is digitally sampled and thus aliased, it can be thought of as a two-dimensional probability histogram of the points in the set.
The renderer also colors the points where the color is a function of the 'velocity' of the system, or the Euclidean distance between successive points, a purely aesthetic decision. The intensity is the probability, so bright pixels are where many points are located.
######Some images:
These are 600,000 points per frame:
<More to come>