I have the following image which contain images ordered and scaled according a rank value, the biggest having a rank of 1 and the smallest a rank of 77:
I would like to give smaller ranks more 'weight', so they become a little bigger.
The logarithm seems quite interesting but the problem is that I don't know how to 'contain' it in a 0.0 to 1.0 space:
Do you know what formula could be used to give smaller values more weight ?
If your purpose is to shift the values from $[1,77]$ to $[0,1]$ while increasing the relative weights of the smaller ones comparing with the larger ones, then you can try either one of the following options:
$\dfrac{\log(x)}{\log(77)}$
$\sqrt{\dfrac{x}{77}}$