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The process of making text in Swift change colors dynamically requires several steps:

1. Declare a label containing the text that you want to change colors dynamically.

2. Create an array of colors that you want to use to change the label's color dynamically.

3. Use the UIView.animationWithDuration() function to animate the label's color change.

4. Set the label's textColor property to the next color in the array after the animation has completed.

5. Repeat steps 3-4 until you've cycled through all the colors in the array.

Here's an example code:

let label = UILabel()
let colors = [UIColor.red, UIColor.blue, UIColor.green, UIColor.yellow]

func animateLabel() {
   UIView.animate(withDuration: 1.0, animations: {
      self.label.textColor = self.colors.first // Set the initial color of the label
   }, completion: { finished in
      if finished {
         self.colors.append(self.colors.removeFirst()) // Move the first color to the end of the array
         self.animateLabel() // Repeat the animation
      }
   })
}

In this example, the animateLabel() function uses an array of colors (colors) and the UIView.animationWithDuration() function to cycle through the colors in the array and animate the label's color change. The function starts by setting the label's initial color to the first color in the array. Once the animation is complete, the function moves the first color to the end of the array and repeats the animation with the next color in the array. The process continues until all the colors in the array have been cycled through.