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I would like to do the same thing that we can see from the picture but with Mathematica. The problem is that I am only an high-school student which try to do this. It would be appreciated if it could be kept simple.

enter image description here://i.sstatic.net/oBO7d.jpg

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    $\begingroup$ We just had a slew of conformal mapping questions, which is a form of what you seek. My Ellie is fairly easy to transform, but it was a lot of work. I'm not about to repeat it for your figure. (All the examples there are in terms of complex-number transformations, but it would be easy to revise them from $z = x + i y$ to $(x,y)$ terms.) $\endgroup$
    – Michael E2
    Apr 28, 2022 at 16:49
  • $\begingroup$ This is possible in Maple (see transform and that example). It should be noticed that transform works with non-conformal mappings too. $\endgroup$
    – user64494
    Apr 28, 2022 at 18:11
  • $\begingroup$ { Cos[0.82 x] + Sin[0.33 y], 0.75 - Cos[0.33 x] + Sin[0.82 y] }, {x, 0, pi}, {y, -pi/2, pi/2} $\endgroup$
    – J.Doe
    Apr 30, 2022 at 22:02
  • $\begingroup$ I thank you all for the help. $\endgroup$
    – J.Doe
    May 1, 2022 at 11:05

1 Answer 1

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One way to approach this is to start with your image and then warp it with ImageTransformation... since you didn't provide an image, I'll use a random one grabbed from the web. The two Sin functions control the warping of the regular grid lines in the original picture.

img = Import["https://i.sstatic.net/W2kZh.png"];
ImageCrop[ImageTransformation[img, 
      # + {.02 Sin[ 20 #[[2]]], .02 Sin[ 20 #[[1]]]} &], {150, 160}]

enter image description here

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