User blog:KthulhuHimself/L-system functions, and why they might be fast growing.

Lately, I've thought of devising a simple uncomputable function, Ls[{m}r1|r2|...](n).

Ls standing for L-system, the function takes any L-system, and depending on the number of iterations, will give an output equal to the number of intersections that appear in the L-system itself.

Ls[{m}r1|r2|...](n) is the function, where m, r1-rx, and n are variable.

m stands for the base angle the L-system will turn with.

r1-rx represent the rules that define the L-system itself.

n is the number of iterations.

Ls[{91},X=Y-Y-|Y=X+X-UU|U=++X-](n) is quite a interesting case, as it seems to grow in a peculiar pattern.

Here are its first few values:

n=1 is 0

n=2 is 0

n=3 is 0

n=4 is 1

n=5 is ~7

n=6 is around 30-50

n=7 is around 110-120

Other L-systems can inhibit faster rates, such as  Ls[{101} X=Y--YY|Y=X+X--U|U=+X+YYU ](n)

n=1 is 0

n=2 is 7

n=3 is 6

n=4 is well over 30

n=5 is around 40

n=6 is somewhere around 130

While this might not compete with ANY other uncomputable function, this is still quite interesting.

I'd like your feedback.