What your defining seems to me to be a NOT map or else it is a mere random map. There is no consistent definition of an "inconsistent" map otherwise, IMHO. Please explain how I am wrong. ;-)
I wanted to have a sequence that does not accumulate net information or have an rule that is itself net information. A random sequence has to check to see if its pattern fits some test for randomness. A path wherein each step is inconsistent with the past sequence seems to meet the requirements I desired.
Why not a map that is "a path where the information associated with each step is consistent to some degree /delta with the information available about the prior steps"?
In my opinion any such rule is net information.