What actually determines the price of a stock? (in realtime, other than supply and demand)

I'm looking for the practical answer that goes beyond 'supply and demand'

When you think of a stereotypical 90s movie about stock brokers, it is always portrayed as a hectic large office with people all tuning in to this magical big screen that tells them the stock prices, which are fluctuating every split second. But what actually determines those prices? Who or what decides that company x will now be priced 0.0001 cent higher than a second ago. Those numbers don't magically appear, there has to be either a person or an algorithm deciding what those numbers will say. I'm assuming nowadays it will be an algorithm, one that factors in supply and demand. But who makes the algorithm? And how does it account for the various streams of information? What factors are part of the equation?

Thank you