http://www.perlmonks.org?node_id=899463
clinton has asked for the wisdom of the Perl Monks concerning the following question:

I'm trying to come up with a formula that I can use to represent distance from a central point, and will return a boost value in a range, eg 0..10.

This formula can accept two (or maybe 3) variables:

1. importance: this controls the upper limit of the range, eg 0..10, 0..100
2. radius: ie any distance within this inner radius should be pretty much as important as any other point within this radius
3. dropoff: (optional) how quickly the boost should drop off as distance increases

My basic formula is:

```
boost = importance / ((radius + distance) ** dropoff)

For instance, an importance of 100, a dropoff of 0.5 and a radius of 0 gives me a curve like:
```
16   : @@@@@@@@@@@@@@@@@@@@@@@@@
32   : @@@@@@@@@@@@@@@@@
64   : @@@@@@@@@@@@
128  : @@@@@@@@
256  : @@@@@@
512  : @@@@
1024 : @@@
2048 : @@
4096 : @
8192 : @

But with a radius of 1000, I get a much smaller range:
```    16   : @@@
32   : @@@
64   : @@@
128  : @@
256  : @@
512  : @@
1024 : @@
2048 : @
4096 : @
8192 : @