How do you "simulate" different frame rates to see that "it does not produce results"
My old screen died so I bought one with 240hz and I switch the hz up or down in the settings to test and compare how far the cubes go apart over the course of the movement across the screen, as that should be the same if it were framerate independent. Also there is the Framerate mode in the advanced options where you can have the game running as quick as it possibly can, which is somewhere around 2000fps in my game. I was already aware before that something isn´t framerate independent, but having the new screen kind of put a little more priority on it.
You explained what you did, as far as code goes, but I do not know what mechanic you are attempting to achieve and what result.
The object with tile movement that stutters is the (usually invisible) player object. The other one that follows is the actually visible sprite of the player. I just don´t want the player character to visibly stutter when moving, as it would if I were to just pin the sprite to the player object. So they are seperate and while the player object is waiting for the function to go through, the visible sprite has time to catch up. (But overall it should always be just slightly behind)
As dop pointed out, dt is working just fine and the dark blue square moves as it should. So the question now is how to make the cyan square move framerate independent. Artificially extending the pause from 1 tick to 0.03 seconds should do the trick, but it doesn´t work.
Here´s a comparison with the 0.03 second delay. I´ve also timed the movement of the cyan square at different fps and it takes 4.3 seconds at 60fps, 4.2 seconds at 240fps and 4.1 seconds in "unlimited" mode. So it is not framerate independent.