The second graph has a huge jump because the left side of the area I'm taking points from is a boundary between two very distant parts of the curve. In any space filling curve you will be able to find arbitrarily large jumps like this.

The difference would be more pronounced on a non-log scale, except the huge numbers at the top of the range would squish the graph down so you couldn't see what was going on.

The first graph isn't just not continuous, it's not even 1-1. (I'm ignoring the fact that is also discrete so that any formal sense of 'continuity' can't exist. Even if you tried to make it continuous by filling in the gaps it would be impossible.)