Hi all, Just applied to join and Rich mentioned that he invites people to post a bio, which I had effectively created already in the mail to validate my address, so here it is for all: My name is David Makin and a fellow fractal artist and mathematician (Kerry Mitchell) suggested I join this list - I am a Fractal Artist and programmer and a three times winner of the International Benoit Mandelbrot Fractal Art Contest: http://www.fractalartcontests.com/2006/ http://www.fractalartcontests.com/2007/ http://www.fractalartcontests.com/2009/ You can see my work here: http://www.fractalgallery.co.uk/ http://makinmagic.deviantart.com/ http://www.youtube.com/user/MakinMagicFractals As for the maths, my primary interest is in anything fractal related but IMHO that actually includes just about any math I can think of ;) I am only formally educated to UK "A" level in maths (back in 1980) and by trade am a programmer - I was a late starter to programming as I only came into contact with it at age 20 when I read a BASIC manual and was immediately hooked (my first thought was "I should be doing this, it's so easy") I'm essentially self-taught with respect to programming, my most prominent commercial software was "Crystal Dragon" on the Amiga (a Dungeon Master style RPG) in the late 90's (unfortunately released just as Commodore disappeared due to their stupid decision to go to a console instead of improving the Amiga). The next life-changing event was getting hooked on fractals courtesy of Fractint in April 1999, boy do I wish I'd known more about fractals when I first started programming - I don't think the render times involved or low resolution would have put me off even on my old Dragon 32 and 64 (6809cpu). The main (formal) gaps in my maths relate to more recent stuff like group theory, not something even included at degree level in the early 80's I think (or so my cousin told me - he did maths at Oxford). I am particularly interested in anything related to the mathematics of 3+ dimensions - especially in finding a true "field" of 3 or more dimensions (I've been told all possible 3D fields have been shown to be merely holomorphic? to complex numbers but I don't know the details). For anything public with respect to my maths and programming there are my posts at http://www.fractalforums.com/ where I am a moderator and my formulas for Ultra Fractal in the UF formula database (all "mmf") here: http://formulas.ultrafractal.com/ Oh - also before moving to using Ultra Fractal I wrote my own 32-bit DOS fractal generator "MMFrac", a rather clunky interface and only single layer rendering (except for bump-map mode) but pretty advanced for 2000-2002 in that it eventually included 3D fractals (parallel and perspective projection to 2D) :) Still available on the web but only of interest for those who can run full-screen dos without using dosbox. OK enough about me, does *anyone* know of a 3D or higher mathematical "field" satisfying all the axions on Wolfram here: http://mathworld.wolfram.com/FieldAxioms.html Or does anyone know that there's a proof that no such field exists beyond 2D (i.e. complex numbers). Thanks for reading. Dave