If you are not interested in the mathematical underpinnings, you can skip this explanation and see Centripetal Taxation in action.

This Centripetal Taxation system is based on an integral of a sigmoid function. In a perhaps too-elliptical paper I wrote a while back I originally chose the Logistic Function as the sigmoid, mostly because its range is naturally in the unit interval, . I now use a simpler sigmoid function with a range in the unit interval that does not require (possibly high) powers of .

Here is the sigmoid function:

whose integral is:

We now need to select a value for the following:

and choose a value for such that :

We then set the following:

and define this:

Now we're ready to calculate a tax: