tag:blogger.com,1999:blog-8613785.post111148515595535697..comments2024-01-17T10:32:51.673+00:00Comments on Rupert Rawnsley's WebLog: Drawing Fractals With Interval Arithmetic - Part 1Ruperthttp://www.blogger.com/profile/07338870148803242763noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-8613785.post-1147263641968788052006-05-10T13:20:00.000+01:002006-05-10T13:20:00.000+01:00Hi Adam,Thank you for taking the time to comment o...Hi Adam,<BR/><BR/>Thank you for taking the time to comment on my interval Mandelbrot work.<BR/><BR/>Regarding your question about the <A HREF="http://math.bu.edu/DYSYS/explorer/def.html" REL="nofollow">main cardioid</A>:<BR/><BR/>The area marked in black in my image should be regarded as “definitely in” the Mandelbrot set. Areas with colour have no mathematically significant status (apart from not being definitely in). Therefore the main cardioid could still be in there somewhere. It is possible that, using the interval algorithm, there is too much rounding noise to cleanly resolve the edges of the main cardioid.<BR/><BR/>I have extended this work in a <A HREF="http://rupertrawnsley.blogspot.com/2005/06/drawing-fractals-with-interval.html" REL="nofollow">second paper</A> that introduces two new states to the colouring: “definitely out” and “indeterminate”. If the main cardioid intersected the region labelled “definitely out” in my image, I would concede that an error must have occurred.<BR/><BR/>I would welcome your comments. From your website it is clear that you know a lot about fractals, and I am keen to expose this work to close scrutiny.Ruperthttps://www.blogger.com/profile/07338870148803242763noreply@blogger.comtag:blogger.com,1999:blog-8613785.post-1145802019539029482006-04-23T15:20:00.000+01:002006-04-23T15:20:00.000+01:00on your image there is no main cardioid, so I thin...on your image there is no main cardioid, so I think that your image is not good.Anonymousnoreply@blogger.com