The Fibonacci-series in a binary representation
Tuesday, March 8, 2011 10:45:38 PM
math in general. Although i have a theory, or let's say mind game, that it may
be possible that mankind confides in a false numbering system. In this mind game
there are no negative numbers, and i came to that studying the Fibonacci-series,
the golden rule, Phi and its reciprocal. Please don't think of me as an madman,
it's just a mind game, remember.
The Fibonacci-series is a golden rule in some way for me, and as some others
believe for nature. Nature is very important for me and i try to live "with"
instead of "against" nature, organized in a nature foundation, trying to live
unwasteful (cool word) and beeing respectful towards my master and ceator
nature.
Since a while i wondered how a binary representation of the Fibonacci-series
would look like and some days ago i used my lunch-break for the finding out. The
break was too short and i was too hungry to get a result in only one break, so i
continued the next day. I did it manuall on a grid-paper with a ball-pen and the
windows-calculator (unfortunately i have to use windows at work).
Long time ago i wrote a small python-program to generate the
Fibonacci-series and added recently the output in binary representation
printing out zeros and ones. My first handmade representation an that grid-paper
where just filled boxes, which look great. Now i am searching for a combination,
maybe i use gimp and it's python-interface for that or ask someone to do that
for me, because i am very busy in present days, but altough very curious.
My curiosity overruns me an so i tried to digitalize the binary
representation with the gimp. I have chosen the rows for the Fibonacci-numbers
and the columns for the binary numbers 1,2,4,8,16,32,... and so on, as in my
first handmade representation. In this (let us call it a) fractal i detected
patterns, symmetry, re-occurances and everything other appear a good fractal is
"made" of.
My first handmade representation is up to the Fibonacci-number 75025 and has
25 or 26 rows, i am not sure if the series starts with zero or one. The next
attempt should have about 100 rows and i wonder when my computer start to
calculate incorrectly by dealing with such large numbers. I can check this
easily be the first binary-column representating the binary 1, which has a
certain pattern, at least in the first 100 rows or Fibonacci-numbers.
I never tought about the naming of this represenation or fractal, it always
was the Fibbin (or fibin) for me, a constructed shortname from "Fibonacci" and
"binary".













