While designing a UI where data converges toward the right value over time

While designing a UI where data arrives over time in groups of 2, 5, and 10 and gradually converges on the correct value, I wanted it to feel friendly to human users while still giving them a sense of concentration. I tried a number of things and eventually found a compromise that felt right.

1. I constrain the magnitude of each individual numerical change so it never jumps too far at once.
2. I make that magnitude shrink gradually over time.
3. Within that allowed magnitude, I intentionally apply a random value.

The human brain is a prediction machine. It tries to find patterns even in things that look random. I learned that satisfying that tendency is effective for keeping a user focused on the screen.