The issue of Brownian motion during development is completely out of the question since, for sure, the film was agitated during development, which moved the silver particles around much more than Brownian motion would.
So, all that leaves is the Brownian motion of the silver halides during image formation. So, the silver halides are charged particles, ions, and they are converted into neutral silver atoms by the photon-energy of light, which causes them to move and aggregate, which forms the image. Not all of the silver halides get "activated." Some of them just stay as silver halides, and they have to be washed away in the fixing process. But, to what extent is Brownian motion of silver halides occurring within the gelatin medium?
Remember what Brownian motion is: it is the random motion of the atoms within the medium in which the particles are suspended, colliding with the particles, crashing into them, and thus moving them.
The usual examples of Brownian motion that are given is dust in the air, and the original example by Robert Brown was the movement of pollen grains in water. So, in those examples, the mediums are air and water. Those are the fluids involved.
And we know how molecularly mobile air and water are. Liquid water has no shape. It takes the shape of whatever vessel it is in, up to the level that it fills it. So, it has volume limitation, and it is affected by gravity. Air is affected by gravity too but it is extremely light, taking 800 bottles of air to equal in weight 1 bottle of water. So, the effect that gravity has on air is to cause increased air pressure close to the ground. But, that said, air will still "fill" whatever space you put it in.
But, in the case of film emulsion, the Brownian motion would be the movement of charged silver particles from being struck by atoms within the gelatin. But, two things to consider about gelatin: one, it is highly viscous, and mediums with high viscosity have much less molecular movement.
"Brownian motion becomes progressively less prominent, as the particles grow in size or the viscosity of the medium increases."
Then, the second thing is that gelatin is highly complex, consisting of proteins, which are very complex. Proteins are thought of as long chains of amino acids, but that is only the primary structure of the protein. There is also a secondary, tertiary, and quaternary structure to a protein. The secondary structure involves the way it forms a helix; then tertiary involves the way the whole structure bends and folds into a three-dimensional form. Then, quaternary refers to the presence of separate distinct subunits within the protein, each of them doing all of the above. So, proteins are very VERY complex molecularly.
Gelatin is actually MORE complex than that because in gelatin, the protein molecules actually stick to each other forming a complicated matrix.
"You can think of it as a giant mixed-up jungle gym of little protein molecules all sticking together. The water molecules get caught up inside this matrix so they can't just drain out."
And, it makes gelatin a semi-solid, does it not?
So, what we are considering is the random motion of silver halide particles from being stuck by moving molecules from within the gelatin. But, how much molecular movement can be going on in gelatin compared to air or water?
And that is why Brownian motion is not a "problem" in photography, assuming the film emulsion and everything else are prepared properly. TO ATTRIBUTE SPECIFIC DEFECTS OR ANOMALIES WITHIN A PHOTOGRAPH TO "BROWNIAN MOTION" IS INSANE. You hear me? It's insane.