Space the dots out more. Don't let them get close.
  * Still not sure if I want to do this

Rotate the dots around the page in a circular pattern.

Make a better points data structure with x and y keys.

If lines make a connected polygon, shade the inside of it with the average color
of all vertices composing the polygon. The more distant the points (and the
larger the polygon) the more dark the color is shaded.
  * Hard. Not sure where to start with this.