Do computer simulations of the visible universe take into account the current position of stars considering the speed of light?

When one goes to a planetarium or watches a documentary, quite often we will be shown a 'flying' simulation of the visible universe, however the cone structure that this simulation portrays appears to show sections of the universe as empty which leads me to believe that we are being shown where the stars and galaxies that we can see are positioned in the night sky.

I am wondering if there are any simulations of or indeed if it is even possible to display the 'actual current' positions of the stars and galaxies that we can see considering their trajectory, distance and speed through the universe and the speed of the light that has been emitted and has travelled to us over time?