Imagine we have a list of ordered numbers $L = (1, 2,\dots, N)$.
I want to add an arbitrary amount of "disorder" to that list. For instance:
Adding a little bit of disorder would permute a few neighboring numbers
Adding more disorder would permute several numbers, many of them not neighbors
Adding maximal disorder would permute all the numbers
Ideally I would like to use an algorithm that has a sound statistical/information theoretic foundation.
I am not sure about how to search for this. I have tried Googling things like:
- Tunable degree of shuffling
- Generating random lists of numbers with a given entropy / Kullback-Leibler distance
- Generating a list with a given level of presortedness
Note that the solution is not just shuffling a given percentage of the numbers. When disorder is small, the shuffling should occur among numbers that are close.
The process I am trying to model is akin to "shaking." Imagine I have a number of casino tokens ordered one after the other on top of a one dimensional table. Then I shake the table along its dimension and see in what order the tokens landed. The tunable degree of disorder I want to model corresponds to how much I shake the table.
Any ideas? Many thanks!