Permanent ink refers to a very specific type of ink used in permanent markers. It requires the use of toxic chemicals, and it is not very easy or safe to make at home. You can prepare indelible ink--ink that can not be washed out by water--out of other ingredients. Here is one recipe for a resilient, blue indelible ink.
Boil 19 parts water water in an old pot that you don't mind staining. Stir one part borax into it as you heat it.
Stir in two parts of gum shellac until it dissolves. Gum shellac, also known as gum lac, is a gummy excretion traditionally used as shellac. Nowadays, other compounds are used for most shellac, but they may not work well in this ink. Make sure to get the right stuff.
Let the water cool. Filter it through a coffee filter or some other kind of filter paper into a mason jar. Set it aside for now.
Mix one part gum arabic into two parts water. Stir or shake it around until it dissolves.
Pour the gum arabic and water into the mason jar with the first solution. Add one part powdered indigo. Cover the jar and shake it until everything dissolves.
Make sure that everything is at a cool temperature before you add the indigo.
Be sure not to spill the ink!