It starts small to avoid hogging resources. The screen after resizing to show more detail. Now we have zoomed in with the mouse, and increased detail to see the benefits of residual point accumulation. Notice the grayer colors in the less populated areas. Decreased the intial x to .001, allowed to see ALL iterations, and zoomed in on the initial path to see the oscillating patterns.
Saturation is higher here to make the fine lines easily visible.
As I first began, I got to thinking about some of the methods students were using. I felt this to be unnecessarily computationally intensive. In addition, I wanted the user to be able to see that near attractors, the points are close together. But there was no OpenGL drawing mode that would allow for this. The two problems prompted a single solution.