Still life frequency distribution hypothesis

[Rhombic]

The rule B2-a3-i5y6c7e/S125y6c7e got me thinking about still life distributions. Other similar rules would probably also work but I expect the results to be pretty much indistinguishable from this one in any case.

Only Lx1 polyominos are strict still lifes.
After trying to find an exponential association between frequency and L (length of still life), I have found that maybe it's actually much much closer to the following relation:

ln(F_L) = k + t·e^(-mL)

so
F_L = e^k·e^[t·e^(-mL)]

where F_L = occurrences of still life Lx1
--------e^k is proportional to the total number of still lifes (so e^k = constant*#TotalStillLifes)
--------t is just a number related to the horizontal translation of the function
--------m is related to dF_L/dx, so the gradient
---and L, as mentioned before, length of Lx1 polyomino still life

as you can see, asymptote y=0 for lim L-->infty

I know some members like to get quite into these sort of demonstrations, so I'd like to see how far off this is from reality. I'll leave apgsearch getting some more soups in the meantime.