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Why doesn't JPEG file format follow indexed color technique?

Besides Knut’s argument that indexed color cannot represent color gradients well, we can also look a the compression method. The JPEG compression relies on similarity between neighboring pixel colors. ...
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What happens when you read and save the same JPEG image again over and over?

JPEG is lossy compression, and it is allowed to do anything deemed beneficial in representing an image as accurately as possible using the minimum amount of storage while keeping cpu load in check. ...
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Why doesn't JPEG file format follow indexed color technique?

Because JPEG is for «natural images» containing smooth gradients, while indexed color is great for many kinds of artificial images containing sharp transitions and a single color background.
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