This Curve Looks Simple At First, But It Gets Complicated Quickly

If you look at the white lines that represent the curve, a point comes when the details are so small that each and every point is covered or apparently appears to be covered by the curve.

P.S. I was wondering if this curve is an example of a fractal.

it is touching every point of graph....

If you carefully study the curve, it is like you are continuously zooming out of a figure that has infinitely small details. So for every point you look at there will be revealed another point that is halfway smaller than that. Ultimately you will be covering the entire square as the figure becomes more detailed.

if we think a sphere having some radius and we want to change that sphere in to a point then sphere have to travel (volum wise compression)all the points in its path to become a point...same way we can think about given curve

The curve joins all the points at a certain time and that time is when the graph is completely white and there are no more points on it.

The curve is in moving position . and in a restricted area only. so it covers unit place of the surface

if you look at the image you may have seen that the curve trought every point

Basing on the figure..it gets smaller and smaller until all the points are covered.

another way to look at this is: if we start from when-the-graph-is-infinetely-zoomed-out and now go on zooming-in, it will always appear that the graph covers all the points (no matter how much we zoom-in), which sounds contrary to common-sense. But that's what 'infinity' is famous for, isn't it? :)