I think you've all seen the sequential flashing of an airport's runway lights when approaching an airport. The flash sequence appears to be wired so that the lights always "run" towards the end of the runway.

Now imagine that you approach an airport in a small plane and see that the runway lights are running away from you. You land, then take off immediately and look back to the runway. The lights still run away from you, now towards the other end. While on approach the lights moved in the same direction as your airplane, they now seem to go into the opposite direction.

What might be the explanation for that phenomenon? Does the tower always change the direction of the light sequence depending on whether an airplane is taking off or landing? Or could there be another explanation?

suddenly i thought of hat phenomen which occurs when wheels turn fast. they seem to turn backwards

Only in a movie. You never see them turn backwards in real life.

But I give another hint: You make a 90 degree turn and after some time you again look back to our hypothetical airport. In far distance you're now seeing the runway from the side. The runway lights now don't move anymore but appear to flash synchroneously!

Maby the lights dont flash with the same light into all directions.
(they are flat anyway, for savety reasons)
Such that only a 45degree angle is lighted up.
This way the plot can see if he is heading toward the runway, of is off course.

Such a system exists, but with another sort of lights. The runway edge lights of airports don't use different lights for different angles.

lol, sounds like the time and distance could be the reason (not really). The lights more far away spread the light earlier but are more far away, so the light needs longer to get to the person standing and watching there, and so the closer lights are seen first even if they flash later
But since light has no speed on earth because its so freakin fast this can´t be the reason.

So maybe the light is getting reflected by the hot gas and particles which came out of the plane while landing. So we get a fata-morgana on the airport. And since fata morganas are mirrored the light the most far away and the closest get switched their positions.

Or 3.) The brain is still thinking the light goes away, even if the eyes see something different the brain is too lazy to correct that and uses as always the short before saved memory.

Yes, an effect of the finite light speed is an interesting idea. And the flashes indeed appear to move very fast - they run over the whole runway distance in a split second. But on the other hand, the speed of light is very high - 300.000 km/sec. Surely we can't visually see light from closer light sources arrive earlier... or can we?

If the runway is 300.000 km long, you would see a delay of 1 second,
With a 3 km runway that is a delay of 0.00001 seconds,
so this cant be it.

If the light is in a prism, the aircraftmovement (up down)
will result in the lights changing it brighness with
a changing hight.

My theory:

Imagine rendering this. When you are moving away from the runway, the lights positions would apear to move up in the y direction on your screen. This is because you are going up so the distance between the lights on your screen gets bigger (it would be biggest if you are right above the runway). Vice versa for approaching the runway. To envision this better, choose two points on your table (put your fingers there) and now look at it from above and from the side. When looking at it from the side, the distance between the points on the y axis of your viewing plane is 0.

I think our brain sees the light as a different object when it is on or off. While it is on, the light seems to move up on your 'screen', then it goes off ('dissapears') and goes on again: 'reapears' (if it would continue to move 'up' at that speed) at the position of the next light.

Now if the lights would be on all the time we would see this as just the effect of going down but because of the flashing they seem to move away.

never thought of this but it must be some sort of optical illusion.
i would guess that the brain/eyes takes longer to register smaller lights/objects so it seams that more distant lights have a decay though all lights are lit at the same time.