general relativity - Visualizing GR spacetime distortion in 1+1D spacetime instead of 2D space

Usually spacetime distortion due to mass in GR is visualized as a rubber sheet distorted under some massive object, like this:

^source

or as shown in this link.

But what has always bothered me is that this description doesn't take into account time. As I understand, it's the whole spacetime which is bent, not just space. So I'd like instead to see a visualization of spacetime bending with time taken into account. Something like this:

^{source video}

Here however the gravity field is homogeneous, and I'd like to see it more in the scale similar to previous image of bent space, so that it'd be visible how distortion is becoming smaller with distance from the object.

Is there any such visualization?