This is decent. I personally wouldn't include Texas nor that much of Arkansas in the Deep South, but I can see the arguments for it.
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there are plenty of ways to slice this, but from my travels, however limited, I would argue that much of Texas is definitely "Southern" in much the same way as most of the Deep South is Southern, but Oklahoma is absolutely not Southern at all. Texas shares a lot with the SW as well, but anything I-35 and East is really nothing like NM or AZ. I have no idea why Houston is its own section, especially Overall this map seems mostly ok.