I've been reading Godel, Escher and Bach. In chapter V 'Recursive Structures and Processes' there's a recursive function given for Diagram G as:(adsbygoogle = window.adsbygoogle || []).push({});

G(n) = n - G(G(n-1)) // for n > 0

G(0) = 0

I can codify the Fibonacci seq that the diagram creates as:

$f=1,1;foreach($n in 3..30){$f += $f[$n-2] + $f[$n-3]}

or say that the total node count for rows up to n will be the actual node count on row n+2.

But, I'm not sure what he's trying to say with the function above? I gather it's more a statement about the overall geometric structure rather than an individual item in the Fib. seq.

But how can n - (anything) produce G(n)? Is n an integer - the nth order, or the whole diagram?

Many thanks,

Duncan

**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!

# GEB - Diagram G recurive definition

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