Tony Hanmer <a.hanmer@gmail.com> wrote:
All the recent developments with orbital rendering in Fractint - for which I say well done, beautiful, some pars from me to follow soon - also makes me think of another fractal type composed of curved lines, namely Klienian Groups, e.g. as at http://klein.math.okstate.edu/IndrasPearls/
Great link! Thankyou, Tony.
It would be great to have these incorporated into Fractint. One suggestion - another dream of mine - would be to enlarge the L-systems possibilities to enable L-systems lines themselves to be curved, e.g. according to various user-input equations for curved lines such as the circle and parts of it, spirals, parabolae, hyperbolae, etc.
Yes! That would be nice. You seem to be the local expert on L-systems: might you answer a question about them? Are they, in general, the iteration of geometrical shapes, thus not necessarily made up only of line segments, nor necessarily only at integer divisions of 360 degrees orientation? I think you were implying in some of your previous posts that maybe the Mandelbrot set could be theoretically rendered as an L-system. I suspect that it can, but obviously being able to plot curved shapes would help achieve that. Also, being able to use more complicated formulas to specify the base shape's size and direction would help. Perhaps a parser to user-specify these attributes? ---Hiram