How do stock prices change throughout the day?

I understand the company values a stock and a sets a price initially.

I understand the value fluctuates based on supply and demand.

But I don’ understand how it fluctuates? What determines the price of a stock throughout the day? Are they programmed a certain way? Do they all have a ratio or something? I don’t understand what is changing the stock price and by what means or value it changes to.

Edit: is it the company changing the price, the NYSE?