CANDY Function

Here is the 3rd fastest growing function ever defined: the CANDY function. In this paper, I will show the rules to the CANDY function, small values, and how to evaluate it yourself.

CANDY function rules:

The CANDY function is a variant of and significantly more powerful than the xi function, defined by Adam P. Goucher. Like, the xi function, there are beta-reduction rules. Here are the 5 rules of the CANDY function (rules ARE case sensitive):

C: Ca -> NULL
A: Aab -> Aba
N: Nabc -> Ncbc
D: Dabcd -> Ddbdcd
Y: Yabcde -> Yebecede

Also, we use the infinite sequence YDNAYDNA...

As you can see, each "level" or step down of the CANDY function almost doubles the number of letters. So, now it is time to get started with small values by spelling CANDY starting with Y.

Small values:

CANDY(1):
Y
CANDY(1) = 1

CANDY(2):
YC
CANDY(2) = 2

CANDY(3):
YDC
CANDY(3) = 3

CANDY(4):
NDYC
CANDY(4) = 4

CANDY(5):
ANDYC
ANANYCDC
AANANYAYNYAYNY
CANDY(5) = 16

Good luck,
Wythagoras