# How do I make a spacetime curvature grid like this (the black hole one)?

I wanna make a grid like the black hole one but with bigger size and more subdivisions. I tried using the Envelope Distort tool and dragging the anchor point but the result is pretty pointy, is there any other way to do it in illustrator? Or any other software can help me do it faster?

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Illustrator can make the funnel as a surface. You can get it by applying 3D effect revolve to a curve. You can get the half-funnel by using only 180 degrees revolution angle. The grid on it can be mapped art. A little more flexibility can be achieved if one uses revolution effect in a 3D drawing program, but at least the half-funnel can be got as easily in Illustrator. The next image is an example of the mentioned half-funnel.

The grid is problematic. Very few of us, who draw, make layouts and edit images know what's the meaning of the grid. It's easy to waffle for example "it presents space and time curvature caused by mass". Such description is useless for drawing it. I tried to read more of it to get the idea, but the reading stopped to cryptic sentences written in an unknown script. A random sample of the script:

It could as well be a magical engraving on The Nibelungen Ring.

For me the blue gridlines look like there were originally an uniform rectangular grid printed on a plane. Then someone put a heavy round bullet on the plane which started to stretch. The plane material is so easy to stretch that there's finally a deep pouch under the bullet. There's no horizontal gridlines on the vertical edges of the pouch, because their original non-strethed material didn't have any. But just below the bullet there can be a few. Or maybe some of them sink into the bullet - impossible to be sure.

The plane is nearly intact far away from the pouch, but the stretching increases as one goes closer to the pouch and that's shown as curved gridlines. This cannot be achieved by projecting a straight planar rectangular grid downwards because it totally skips the stretching towards the pouch.

The whole diagram shows the bending and stretching of a 2D space (surface) to the 3rd available dimension because we do not have a way to show more dimensions. It's only a metaphor. The script used in the magical engraving above may be the way to talk about all of the needed 4 dimensions exactly, without vague metaphors.

One should map on the surface something substantially more complex than to project downwards a rectangular grid. The geometry distortion problem probably would be easier if the grid was in polar coordinates, but that was not asked.

You wrote you want more subdivisions. I guess you are not talking about the common method to approximate the surface with squares or triangles. Their density and division lines know nothing of the gravity, they are selected only to replace a smooth surface with polygons within the decided accuracy.

Can you perhaps tell in a practical way what the gridlines mean in the stretched version. I assume they should be formed with some rule from an uniform rectangular grid on a straight plane. And it's NOT the straight projection downwards. Nobody can draw anything which somehow presents the effect of the gravity without knowing that rule.

In addition: What's the exactly wanted revolution profile of the pouch and why is it so deep?

If you cannot tell them you ask also an artistic interpretation or scientific knowledge. Those are totally different things than "how to draw" and the respected members probably close your question. But before it happens here's one attempt to redraw the wanted metaphor (no bullet included):

This is a drawing (Illustrator) of a guessed revolution profile and a grid which probably generates the wanted illusion when it's projected downwards. The grid is made by blending straight and curved lines. The revolution profile is drawn with the pen.

My antiquated illustrator version is unreliable with 3D effects and there's not at all the art mapping mode which is easy in this case, so I move the job to a 3D drawing program:

In the left the profile curve is revolved 180 degrees and the grid is rotated 90 degrees. In the right the grid is projected straight downwards.

The viewing direction can be rotated freely and the view can be exported as a 2D image for illustrator. The projected grid can be a vector, but the shaded half-funnel is only a bitmap image. Rendered shapes with lights and shadows cannot be exported as gradient meshes, not at least in any generally available low cost 3D program.

The black sphere can be inserted later in a 2D drawing program. It can be simply a flat black circle. For obvious reasons it cannot have any glosses nor other shading.