From kragen@dnaco.net Sat Aug 29 11:12:52 1998 Date: Sat, 29 Aug 1998 11:12:50 -0400 (EDT) From: Kragen To: "'fractint@lists.xmission.com'" cc: ctm@math.harvard.edu Subject: RE: (fractint) Fields Medal In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Keywords: X-UID: 1577 Status: O X-Status: On Sat, 29 Aug 1998, Joe Pearson wrote: > No, but he seems to have a lot of mentions at the Harvard website. > http://www.math.harvard.edu/~ctm/ It appears that www.math.harvard.edu is a Solaris machine with the TCP bug that makes it nearly impossible to download files from it over a 14.4kbps dialup. (What bozo put that thing in as a Web server?) Fortunately for me, I have a shell account on a T1, so I can circumvent this problem. > http://www.math.harvard.edu/~ctm/papers.html has a list of his papers. > "The Mandelbrot set is universal" sounds like the answer, but it's in > formats I can't read (gunzipped postscript and dvi). On the theory that he put it up on his Web site so people could read it, I have taken the liberty of preparing a gzipped PDF version at . Unfortunately, it's 1,469K after you un-gzip it, compared to the 75K gzipped PostScript version. gzip compresses it down to 124K; WinZip (among other things) can un-gzip the document. I hope that the author has the time and the space to put a PDF version on his own web site, because I'm a little tight on space. Better software tools than the ones I have could probably shrink the raw PDF version to 150K-200K or so. The paper is 19 pages. It begins something like this: The Mandelbrot set is universal Curtis T. McMullen March 13, 1998 Abstract We show small Mandelbrot sets are dense in the bifurcation locus for any holomorphic family of rational maps. 1 Introduction Fix an integer d >= 2, and let p[c](z) = z^2 + c. The *generalized Mandelbrot set* M[d] is a subset of C is defined as the set of c such that the Julia set J(p[c]) is connected. Equivalently, c is an element of M[d] iff p[c]^n(0) does not tend to infinity as n approaches infinity. The traditinal Mandelbrot set is the quadratic version M[2]. Kragen -- Kragen Sitaker We are forming cells within a global brain and we are excited that we might start to think collectively. What becomes of us still hangs crucially on how we think individually. -- Tim Berners-Lee, inventor of the Web