[seqfan] Recaman Video

Dale Gerdemann dale.gerdemann at gmail.com
Thu May 23 16:00:10 CEST 2013

Dear Seqfans,

I've jut put a video on YouTube which should be of general interest here.


I've been playing around with Fibonacci Word Fractals for about  half a
year now and have left a rather messy record of vides on YouTube, Recently
it occurred to me that the Fibonacci word was not necessary  for the
construction of these fractals. One could just as well use a slightly
modified Zeckendorf representation, looking at the positions of the least
significant non-zero digits. This raises the possibility of making
fractals, or at least interesting images, for any sequence that can somehow
be used for a numeration system. I chose to try this idea out with the
Recaman sequence since it is well known and has a quirky definition which
would suggest some difficulty. I tried one other odd sequence and got a a
very nice wire-sculpture kind of result:


The sequence used was: a(n) = 5*a(n-1) - n/2 (where the division is integer
division, throwing away the  remainder.

A while back, Neil wrote that he was working on a math museum. Perhaps the
kind of turtle graphics on steroids that I've been working on would be fun
for young museum visitors).  In any case, I'm not selling anything, I don't
make money from the videos and I'm willing to give away what I've got if
Neill is at all interested.

Dale Gerdemann

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