necchi is correct.
You have a copper plated barrel. The copper plating at the muzzle was removed by whatever you were using leaving the dull bare steel showing thru.
Like the instructions necchi posted say, once that copper plating is deposited, there is no way to get the barrel to actually form the brown rust that most of these guns have without sanding the copper off. That leaves the barrel steel exposed so the process can be started over.
If you want the barrel to look like it presently does you can buy some Laurel Mountain browning solution. Put on some latex gloves and get a small cotton rag.
Wet the rag with the solution and rub it rapidly back and forth on the unplated area, applying pressure while you do this. That should lay down a layer of copper so it looks pretty much like the rest of the barrel.
You didn't ask about it but IMO, your front sight is a hazard. It is a front sight blank that was supposed to be filed to a proper shape.
The proper shape (most will agree) has a nice gentle curve that approaches the barrel towards the muzzle. The rear can either be rounded or left square.
This tapered area will deflect your hand rather than gouge into the flesh if it strikes the sight from the front during loading.
By the way, if the gun was mine I would use some 180 or 220 grit black "Wet/Dry" sandpaper and sand off the copper using long strokes that are parallel with the length of the barrel.
Then I would apply some LMF Browning the right way (without rubbing or overlapping multiple coats) and let the humidity turn the steel into a nice hard brown rust.