Path: utzoo!utgpu!jarvis.csri.toronto.edu!cs.utexas.edu!mailrus!uflorida!stat!fsu!geomag!prem
From: prem@geomag.fsu.edu (Prem Subrahmanyam)
Newsgroups: comp.graphics
Subject: Mandelbrot Observation
Message-ID: <384@fsu.scri.fsu.edu>
Date: 28 Nov 89 17:51:43 GMT
References: <19990@pasteur.Berkeley.EDU>
Sender: news@fsu.scri.fsu.edu
Reply-To: prem@geomag.gly.fsu.edu (Prem Subrahmanyam)
Organization: Florida State University Computing Center
Lines: 19


   Here's an observation I have made that seems contrary to (at least some)
   popular belief concerning the Mandelbrot set.  I read in one of the Computer
   Recreations articles in Scientific American that the Mandelbrot set is not
   self-replicating at different levels.  Yet I have clearly seen identical
   reproductions of it in many places.

   If you look at the "line" protruding from the "head" of M, you will see that
   there is a tiny replica of the big part of M.  Magnifying in on this reveals
   another tinier replica coming off of this head, and so on ad infinitum.  
   Albeit, the "domains" are not identical around the replicas at every level,
   but the shape of the black part is the same.  I haven't tried to zoom in on
   tiny areas of the tiny replica to see if the fine detail is the same, but
   in general, it seems that M, as well as all J sets, is self-similar to a
   high degree.

   Any other opinions, observations about this?

   ---Prem Subrahmanyam (prem@geomag.gly.fsu.edu)


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