Creating 3D halftone wavy effect using any tool
I think that particular image may have been generated by a 3D application. Which one is your choice.
Illustrator can do this to a degree, but it won't easily create the depth of the bump texture. You have to kind of fake it.
Draw a couple random paths....
Select both paths and choose
Object > Blend > Make from the menu.
Object > Blend > Blend Options... from the menu, tick the
Preview box and set the drop down to Specified Steps, then input a number of steps to create a clear transition between the lines without too much space or so tight you can't see any separation:
In the Stroke Panel tick the Dashed Line option and set the fist
dash field to 0pt, then set the first
Gap field to twice the size of your stroke weight. Then tick the rounding options (highlighted in magenta below):
From there it's all a matter of colors..... and repeating the same steps for more shapes.
You can edit the paths to refine where the dots fall, you can alter the blend steps to increase frequency, and you can alter stroke weights to change the size of the dots.
I realize this is not nearly as smooth and doesn't possess the depth of field in your sample. But this is as close as Illustrator can get. And much of the appearance depends upon how long you set it up. This was a quick example and hasn't really been refined to any degree. Adding masks and hiding sections would result in a close to your sample match.