That's rust getting under the clear coat. It follows the gaps in the protective coating and forms those white veins. They are white because aluminum rusts white not brown.
The only way to fix that is to remove the clear, polish out the rust, and recoat them. Most wheel repair places can do that, since the same happens with wheels.
To be honest, it's probably cheaper to get another set. My chrome sidesteps were only about $120. The old stainless ones were $140, but Smittybilt stopped making them.