"SherLok Merfy" <brewhaha@freenet.edmonton.ab.ca> wrote:
Not really, kayos.map is just a tweaked graymap. It is also just intermediary results in my search for excellent fractals that look like suits for cards.
Oh, that explains the name of your .frm "Club_Lambda". Rather than just searching for them, have you considered the possibility of finding excellent fractals with circles in them? Those should be a lot easier to find than shapes like clubs or spades . Then you could morph the appropriate region of the domain complex plane (the "pixel" variable in the .frms) into the suit shapes with conformal mapping. I think I saw you used the "INVERT" command in one of your pars earlier; that's a simple example of a similar process. Around 90 years ago, before _any_ automated calculation was available, Joukowski came up with the process of conformal mapping to warp the (analytically known) velocity field around a circle into the velocity field around a class of (actually quite serviceable) airfoil shapes and still satisfy the flow conditions; people later extended the idea to arbitrary shapes on the complex plane. I don't see any reason you couldn't use the same technique on fractal viewing planes. Some information on conformal mapping is here: http://math.fullerton.edu/mathews/c2003/ConformalMappingBib/Links/ConformalM... BTW, I noticed that "Club_Lambda" uses two complex process parameters just like the Julia/Mandelbrot duality. It could just as easily be extended into the "4 dimensional" format that Jim is using for the Julibrot. (I consider it to be really (or maybe imaginatively) to be 2 dimensional, but by his silence he apparently disagrees, which is okay) In any event the extra dimensions would give you a much wider space to search for your ideal suit shapes. Hopefully being helpful, Hiram Berry