I'm plotting data using circles. I am assigning the radius of the circles to be the value of the data each circle represents. Since the data values get too large to successfully plot in this way I would like to replace this linear mapping between data and radius with a logarithmic mapping, i.e. make the radius of the circle the natural log of the value it represents.
This seems straightforward, apart from values below 1 where the radius becomes negative.
To get around this I am mapping zero data to zero radius, data values below e to a radius of 1, and every other data value to its natural log.
The data is the output of a General Ecosystem Model and the goal of the visualization is to provide a simple view onto the model through time, allowing the user to choose between things like biomass or average age as the sizing factor.
What is the standard practice for dealing with small values when drawing graphical content proportional to the natural log of the data it represents?