I have a parametric function defined by the x and y functions:
x = r*Cos[w_0*t - w_L*t] +
z*Cos[w_P*t - w_L*t]
y = r*Sin[w_0*t - w_L*t] +
z*Sin[w_P*t - w_L*t]
I can change the variables around to see interesting patterns formed by the function. What I want to do is have some sort of plot of this 2-D function where a grid is placed over the plot, and each square of the grid has the total amount of coverage of the function over the grid, meaning the total length of all the the lines passing through it. From the image, you can see that grid 3 has much more coverage than grid 4. That's what I want to quantify, but I really don't know how to attack the problem.
Basically, I want to set my parametric plot flat on a table and see the variation of density in different regions. Thus grids with lots of coverage will have a higher z-value. Perhaps there are other solutions to this than my idea, but I am certainly not sure.