I have a scatter plot where most of the data points are near the origin. The closer to the origin, the more data points one can find. I have tried to use logarithmic scale for the $x$ and $y$ axes to display more data points near the origin. However, one problem is that there are a lot of data points on $x$ and $y$ axis. Using a logarithmic scale will not property display those points on $x$ and $y$ axes. I am wondering whether there are other way of scaling the $x$ and $y$ axes such that I can get more details near the origin, while still able to display the points on the $x$ and $y$ axes.
Note that all the data points range in $[0, 1]$ for both $x$ and $y$ coordinates.
