Originally posted by Eduardo:
QUOTE]This may well be a dumb question, but what happens when the measuring device reaches the Planck length?
Well measuring this purely mathmatical fractal, say after every iteration your measuring device is the length of the shortest line. You start with one line
After the first iteration, the shortest line is L/3 and there are 4 of them so the total length is 4/3*L
Generalizing now there are 4^n lines each of length L/(3^n). n is the number of iterations. below is n=2.
As you do each iteration the length of each segment gets smaller, but the total length of all of them combined is greater. If you do an infinite number of iterations then the length approaches infinite. Assuming the starting length is 1 meter, the number of iterations you would have to do for the lengths of each segment to reach the planck length would be about 73.
So our physical limit can never get smaller than the planck length. At that point the total length will be about 1.3 billion meters[L*(4/3)^n]. Keep in mind that's with L=1meter to start with, and just with this snowflake thing called a Von Koch island.
This website has some info on fractals and some cool pictures that were created using fractals.
plus.maths.org
