Find the BCD difference of a number
Wolfram Language (Mathematica), 89 88 bytes

Thanks to Jenny_mathy for saving 1 byte.

i=IntegerDigits;Max@#-Min@#&amp;[#~FromDigits~2&amp;/@NestList[RotateRight,Join@@i[i@#,2,4],#]]&amp;


Try it online!

This is terribly inefficient, because it generates n rotations of the BCD of n, which is way more than we need. We can make this is a bit more efficient by saving the result of the Join@@ in k and replacing the # at the end with Length@k. That lets us generate a scatterplot quite easily:



I'm really intrigued by the contrast of local structure and overall chaos.