If one wants to plot a variable whose value changes drastically, it makes sense to plot its order of magnitude. That way, the smaller values in the plot aren't squished all the way at the bottom. This in turn "compresses" the axis, making the plot more readable.
Whatif I'm plotting a variable whose value changes only slightly in the domain I'm using? Then I would like to "stretch" my vertical axis, exactly opposite of what the logarithmic scale does. Is there a standard for such a system? I could just raise it to a power and plot that, but I'm looking to see if this is typically done in a certain way.
Best Answer
You can plot with exponential scaling, for example $x = 10^{x'}$. This is equivalent to plotting $\log_b f(x)$ vs. $x$.
To elaborate, consider a plot $P$ to be defined by plot coordinates $x', y'$ and a graph with points $x,y$.
If you want $x'$ to be "shorter" for large $x$, i.e. stretch the axis, you'd set $x=10^{x'}$ and thus $$y' = y = f(x) = f(10^{x'})$$ This is good, if $f'$ is very small.
If $f$ is very small in change, you could go for $y' = 10^y$ instead so $$y' = 10^y = 10^{f(x)} = 10^{f(x')}$$ For very simple functions, say $f = {\rm id}$, you can interchange these equivalently with $\log$'s of the "other axis".