I think some sort of looping is necessary to ensure that the player can't walk around the edge and chart out the entire map quickly, after all part of the idea is to confuse them. What do you think about only looping on specific tiles?
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I think that looping doesn't work because the person will still chart out the map by finding the width/height relative to a point of interest what I think is the issue is if after looping you walk forward and then bump into a wall making you think that the map is wider than is or just drawing the map wrong though some interesting puzzles like having to loop around walls would be fun.