Learn French: Le mien apparaît au fur et à mesure que tu agites le fixateur.

While pendant que just means two things are happening at the same time, au fur et à mesure que adds the idea of proportion or progression. It tells us that the subject doesn't just appear while you shake the fixer, but it appears gradually and in direct correlation to the shaking.

Does au fur et à mesure que trigger the subjunctive?

No, it takes the indicative. You can see this here with tu agites, which is the regular present indicative. This is because au fur et à mesure que describes an objective fact or a real, ongoing action, rather than expressing an emotion, doubt, or hypothetical situation.

Why is there an article in front of mien (Le mien)?

Unlike English where we just say mine, French possessive pronouns always require a definite article (le, la, les). The article and the pronoun must match the gender and number of the noun being replaced. Here, Le mien tells us that the thing appearing is masculine and singular (perhaps a photo print or a document).

Why does apparaît have a circumflex accent on the 'i'?