Self avoiding random walk for pixel modification

Hello everyone. I have a problem, explained below. I expect your kind help, thank you. I have a 2D spatial coordinates of a true colour image. Now I need to generate a self avoiding random walk to modify the pixels. A criteria is to avoid the pixels that have been already modified. How to approach for it? I am new in this approach.

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There are lots of random walk algorithms already layed out within the forum.
Study those methods and try to get a sense of the big picture before starting to implement the algorithm in your code. If you have a specific problem, come back to the forum (or this thread) for specific questions.

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