Date: Sat, 10 Jan 1998 06:25:47 -0500 (EST)
Message-Id: <199801101125.GAA06666@freenet2.carleton.ca.carleton.ca>
From: ao950@freenet.carleton.ca (Paul Derbyshire)
To: fractint@lists.xmission.com
Subject: (fractint) Distance Estimator for any function
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Content-Type: text




Herein is a generalization of the distance estimator method that, by
avoiding using the derivative f'(z), can be easily generalized for any
formula without having to write a new algorithm for it or know the derivative!


In the formula, distest=1/2*log(|z|)*sqrt(|z|/|z'|) where |z'| is the
derivative, replace |z'| with |(z-w)/e|, where w is set equal to z at the
first iteration plus a small value e. (w-z)/e is simply a quantity that
tends to z' as e tends to zero. For Julia types, z is as expected; for
Mandelbrot types, use 1/2*log(|c|)*sqrt(|c|/|c'|), c' approximated as
(w-c)/e, w starting out as c+e.

e must be chosen small (try 1.0e-13) for this to work well.

I tested it; it works. I did it on z^3+c.


--
    .*.  Friendship, companionship, love, and having fun are the reasons for
 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire ao950@freenet.carleton.ca pgd73@hotmail.com

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