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From: kay@warwick.UUCP (Kay Dekker)
Newsgroups: net.graphics,net.math
Subject: Mandelbrot set problem
Message-ID: <2346@flame.warwick.UUCP>
Date: Mon, 4-Nov-85 12:58:01 EST
Article-I.D.: flame.2346
Posted: Mon Nov  4 12:58:01 1985
Date-Received: Sun, 10-Nov-85 08:54:08 EST
Reply-To: kay@flame.UUCP (Kay Dekker)
Organization: VLSI Group, Warwick University, UK
Lines: 28
Xref: watmath net.graphics:1252 net.math:2501
Xpath: warwick flame flame ubu

I've been writing a 'browser' to examine the Mandelbrot set for interesting
areas.  It works fine, except for one thing which I haven't been able to
fathom.

The browser decides that a point lies within the set if its magnitude after
a maximum number of iterations is < 2.0.

I've seen browsers posted recently in net.sources, and examined them to see
if they address my difficulty, but no luck.

How should one choose the maximum number of iterations for any particular
region of the complex plane?  Sure, one can always pick a value that's
"big enough" for any particular view ("big enough" meaning, intuitively,
that not too many pixels are marked as lying within the set when in fact
they aren't), but having such a large value makes the browser far too slow
when that many iterations aren't needed.

Is there a method for finding adequate values for the maximum?  Or must
I continue to rely on trial and error?

Any help or pointers to information gratefully received.

							Kay.
-- 
"Be careful: the system is complex and chaotic, though it
 has many attractive features..."
				_The Pot-holes of the Yorkshire Moors_
				... mcvax!ukc!warwick!flame!kay