Can someone explain the picture to this function for me?

Question

I'm a first year maths undergrad and in my many hours of procrastination before revision, I was playing around in MATLAB when I ended up plotting this function:

t=(0:0.0005:100);
X=t.*cos(t);
Y=t.*sin(t);
plot(X.*sin(10*X.^3),Y)

I understand why the radius of the circle is about 100 here, but why does it oscillate so violently to the point where it virtually shades in the circle area?

Answer 1

Here are the figures for step sizes of 5, .5, .05, .005 and .0005 (with the points joined for clarity):

As you noted, all the points lie in a disk of radius 100. The wild oscillations of the curve traverse horizontally more than vertically (because of the cube term) and naturally cross the center more than points on the periphery.