tag:blogger.com,1999:blog-485664355325189781.post6498685606310471294..comments2023-09-21T21:27:41.264+10:00Comments on I Like Portello: Joyful SymmetryMatthttp://www.blogger.com/profile/02469462608067586388noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-485664355325189781.post-2299664707819974892009-01-05T17:28:00.000+11:002009-01-05T17:28:00.000+11:00yeah, much more sense now. maybe there's a video o...yeah, much more sense now. maybe there's a video or 3d virtual display program somewhere on the net that could work it out.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-485664355325189781.post-82746494181001029732009-01-05T17:14:00.000+11:002009-01-05T17:14:00.000+11:00Hi Paul.The variables x and y are complex numbers ...Hi Paul.<BR/>The variables <I>x</I> and <I>y</I> are complex numbers (of the form <I>a</I> + <I>b</I><I>i</I>, where <I>i</I> is the sqaure root of -1) and so have two parameters each: <I>a</I> and <I>b</I>. A 4-dimensional space is therefore required to render each (<I>x</I>,<I>y</I>) point.<BR/>The curve is 3-dimensional because it's had one dimension restricted by the equation. It's just like in high school maths when you would graph a simple linear equation on x- and y-axes. There you're putting a 1-dimensional object (a line) in a 2-dimensional space (a plane). You can also graph a 2-dimensional surface in 3-dimensional space, etc.<BR/>Hope that makes sense!Matthttps://www.blogger.com/profile/02469462608067586388noreply@blogger.comtag:blogger.com,1999:blog-485664355325189781.post-63401474722704952882009-01-05T13:09:00.000+11:002009-01-05T13:09:00.000+11:00congratulations on getting a symmetry group named ...congratulations on getting a symmetry group named after you. i reckon that's pretty damn cool.<BR/><BR/>i (of course)am not as mathemagic as you are, but the equation you posted seems to be 2dimensional to me, as it has only x and y variables. can you please explain how it is a 3 dimensional object in a 4 dimensional space?Anonymousnoreply@blogger.com