Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!cornell!batcomputer!gdykes
From: gdykes@batcomputer.tn.cornell.edu (Gene Dykes)
Newsgroups: comp.graphics
Subject: Re: Fractals
Message-ID: <7474@batcomputer.tn.cornell.edu>
Date: 27 Feb 89 20:57:46 GMT
References: <160.2404E090@muadib.FIDONET.ORG> <11150@s.ms.uky.edu> <1191@hudson.acc.virginia.edu>
Reply-To: gdykes@tcgould.tn.cornell.edu (Gene Dykes)
Organization: Cornell Theory Center, Cornell University, Ithaca NY
Lines: 20

>> (Description of recursive perimeter check for set points)
>But what if one of the little spidery filaments that connects it to itself
>slips between two of the points you test?  Perhaps this isn't a problem
>in practice...

This isn't even a problem in theory, much less practice.  It's the points in
the set that get infinitesimally thin, not the set of non-set points.  If you
find a perimeter of set points, you can be quite sure that you won't find
non-set points inside.  Another way of stating it is that, although the
set can appear to be disconnected at a given resolution, the non-set points
are always connected.

>What I've been doing instead is testing if the iteration converges, in
>parallel with the usual test for divergence...  It's also faster.
> Check it out.

I've got you both beat.  Do region filling.  The only points in the set that
you'll spend any time on are the ones on the perimeter.  Details on request.
-- 
Gene Dykes, gdykes@tcgould.tn.cornell.edu