I want to create a symlog function that is symmetric around 1 (10^0) instead of 0. The range of output values for the function will be positive: [10^-6 - 10^6] and the input values will be from a linear range (e.g., 0 - 1000).
The expected scale should be like this:
In other words, the scale ticks on the left of the mid-point (10^0 = 1; denoted as "equal" in the above image) should be a mirror image of the right of 1.
To further explain, here is a visualization of a traditional symlog plot that is symmetric around 0:
This is the paper that proposed this scale: https://pdfs.semanticscholar.org/70d5/3d9f448e6f2c10bd87a4a058be64f5af7dbc.pdf
The modification that I need is to be symmetric around 1 (10^0).
I am not very good at math especially log math. Having a hard time figuring this out. Could someone provide some insights as to how best to do it?