What binds pigment to the wall in fresco?

I often asked, what binds fresco paint (natural pigment diluted in water) to the surface in fresco painting?

calcite crystals in fresco painting

Here is a snapshot of the bucket where I rinse my fresco tools and fresco brushes.

Carbon dioxide from the air reacted with the calcium hydroxide (slaked lime) in the water forming a thin transparent crust. Some water had evaporated and you can see that the process restarts once the water surface opens up.

That is exactly what happens on the plaster and binds pigment to the surface.