10.15.2011

Fibanacci * x mod m

found discussion on 3-6-9 on web, if x3 to fibonacci sequence and reduce to single digit or mod 9
the result is octave of "3-3-6-9-6-6-3-9" or "3-3-6-0-6-6-3-0" by modulo method which 0=9, no remainder.
I try to vary multiplier (x) from 2-24 amd m = 9, 11, 12
The pattern of numbers appearance frequency are symetry and beautiful.

10.14.2011

Fibonacci Mod 12 R2

Afetr consider pisano period on pi(m)=24, mod 9 have number 1 & 8 apprear 5 time
also mod 12 , 1 & 5 appesr 5 time. This should be beautiful pattern hidden in mod 12 as well.
Today I found such pattern...


10.09.2011

Fibonacci Pisano Pattern

from pisano period up to m=24.
for m=2,4,11,19,22    there are no zero in the middle of cycle.
there are reverse sequences of 1,2 ,3.......as mark by bold block
there is clearly trand of some data.


Fibonacci Mod 12

After rework on pisano mod n up to 24, I try to draw N-gram mod 11 but not found beautiful pattern.
I relook to mod 12, it has 5 symetrical patterns by using the same method of mod 9 enneagram