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The first thing you need to do is to establish your target (reference) resolution and it is super important that you stick to it during development.
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In a nutshell, even if you follow the strategies outlined by others you still may end up with poor results on different resolutions. During my searches I came across many forum posts coming from people confused about PPU (Pixel per unit), reference resolutions, frame cropping and the list goes on. There are already a lot of tutorials on the topic out there so why bother writing another one? The matter of fact is, there is no silver bullet to solve this issue. If you are an indie developer making a retro style game using pixel art, you definitely want to maintain pixel-perfect graphics across a wide range of resolutions.
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