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My question is what methods are there to "zoom in" on a procedurally generated map using Perlin Noise (or Simplex).

If I have for example this generatedenter image description here

and I wanted to "zoom" into that little red square I drew, how could I achieve something to the likes of this (ugly drawn) example: enter image description here

While staying true to the terrain above? I have heard of 3D methods but couldn't find any meant for 2D maps.

Any advice or help would be appreciated.

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Lets define your noise function for terrain generation as f(x,y).

f(x / 2, y) will set the zoom on the X axis to 200%

f(x, y / 2) will set the zoom on the Y axis to 200%

So, it's f(x / zoom, y / zoom) for your noise function.

This is true for any function in maths.

You can translate your output too.

f(x - 100, y) will move your output by 100 tiles right.

f(x, y - 100) will move your output by 100 tiles up.

To zoom by a factor of z around point (a,b), you'd transform your noise function f(a,b) to f((x - a) / z, (y - b) / z).

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