"cyclic functions" may not be the correct term, but I don't know what else to call them. (only have basic high school math training, no calculus) Here's what I'm looking for.(adsbygoogle = window.adsbygoogle || []).push({});

Given the following series of functions

f(a) = b (step 1)

f(b) = c (step 2)

f(c) = d (step 3)

...

f(n) = a (step n)

Is there a general way to rework these so that you can directly calculate the value at steps 1,2,3 etc rather than having to iterate through all the steps from a to x, something like this?

f(0) = a

f(1) = b

f(2) = c

f(3) = d

...

f(n) = a

This problem arose from a computer program I'm working on and it would be much more efficient to directly calculate the n'th term rather than having to iterate through them all.

Thanks for any help

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Direct way to calculate nth term of cyclically repeating function?

**Physics Forums | Science Articles, Homework Help, Discussion**