Xref: utzoo comp.theory:1391 sci.math:14609 alt.fractals:811 Path: utzoo!utgpu!cs.utexas.edu!uwm.edu!bionet!agate!eris.berkeley.edu!doug From: doug@eris.berkeley.edu (Doug Merritt) Newsgroups: comp.theory,sci.math,alt.fractals Subject: Re: High precision Mandelbrot set Message-ID: <1991Jan9.173200.14621@agate.berkeley.edu> Date: 9 Jan 91 17:32:00 GMT References: <1991Jan8.142354.1732@pegasus.com> Sender: usenet@agate.berkeley.edu (USENET Administrator) Organization: University of California, Berkeley Lines: 24 In article burley@geech.ai.mit.edu (Craig Burley) writes: >In article <1991Jan8.142354.1732@pegasus.com> shaw@pegasus.com (Sandy Shaw) writes: > > My question is : Is there there a way short of using an extended precision > math package to gain further detail upon continuing the zoom? > >Why can't you simply scale up the values (and the math accordingly)? Doesn't work; the values do not always vanish -- i.e. they are sometimes in the form z = (a + b), where a >> b. Scaling would help only for a = 0, 0 <= b << 1, and floating point arithmetic always does appropriate scaling for this case anyway. The above is actually overly simplistic; the recurrence formula can be expanded after N steps into a polynomial of degree 2N, having N (as I recall) non-zero terms, each of which might contribute significantly to the final result (worst case assumption unless you know of some result on the subject). Thus N numeric values in the range |z^2n| <= |a| <= |z| must be summed for the final result, and this is what imposes the requirement for a lot of precision in the mantissa. Doug -- Doug Merritt doug@eris.berkeley.edu (ucbvax!eris!doug) or uunet.uu.net!crossck!dougm