How to show on a graph the change in the distribution of a quantity over time?

Question

Analytics

The graph should show the change in the distribution of ratings among users.
For example, in one day it is:
0 - 100 users
1 - 70 users
2 - 30 users
4 - n users
, etc.
For one day, the graph would be simple, but I need to see on one graph how this distribution changes over the course of a month (for example), when I have distribution data for every day. Sculpting one on top of the other 30/90/365 charts is clearly not an option.
The question is not so much in the implementation, but in how exactly this can be shown visually. But if someone prompts an implementation option, it will be nice.