I am a physicist and I always used to hate the trampoline/ rubber blanket model with all my heart - as it explains gravity with gravity, as it fails to account for the more of space in the center (the rectangles of the rubber blanket become bigger - but from my point of view they had to become smaller as the cubes at the earth in the pic above) and so on. However, some time ago I read a nice laymen - article about how to vindicate the blanket / trampoline model (I add the reference in the comments as soon as I find it). And here is how:
First, you have to replace the small ball (which is under the influence of the big mass in the center) with a car. Second, you have to attach double-faced adhesive tape around the wheels of the car. And now, you try to move this attached-to-space car along a straight way past the center of gravity. But you will experience: It will move in the direction of the center of gravity. Why? Because there is more space for the wheels nearer to the center of gravity to pass over! And what I like the most: If you curve the space the opposite round, i.e. bend the trampoline/rubber blanket in direction to the sky, the space-attached small car will move in a curve in direction to the center of gravity as well! Now, this trampoline model is independent of the underlying gravity! It just explains the curved path of the car by the curvature of the space it is attached to.
Next step: to include the time coordinate. 461
As the rubber blanket model is only 2D (not 4D as the real space time) we have to sacrifice one dimension of space for the inclusion of the time. Never mind, though, as most of the gravitational forces and fields are spherically symmetric - meaning that there is anyways only one space coordinate that matters: the radius r, the distance from the center of gravity. Now, we are bound to move along the time coordinate, we all are and so the space-attached little car is as well. The model with one space and one time coordinate now looks as a river bed where we are all bound to move parallel to the river, even if we do not move in space (=perpendicular to the river). There is a curvature of time that means time runs slower in the vicinity of the river. As a result, the wheels near the river turn more slowly. This is followed by the movement of the car in the direction to the river as time goes by. Gravity.
Welcome back, trampoline model. 461