Jörg>* Bill Gosper <billgosper@gmail.com> [Sep 02. 2014 08:16]: Jörg>* Bill Gosper <billgosper@gmail.com> [Sep 01. 2014 08:00]: [...] Staggering. So somewhere in all that are these three "sevens"gosper.org/IMG_0245.JPGgosper.org/IMG_0246.JPGgosper.org/IMG_0247.JPG Yes, see http://jjj.de/tmp-rwg/ Indeed there are 3 shapes of order 7: http://jjj.de/tmp-rwg/search-r07-curves.txt here a "same = #" means that the shape already appeared at the earlier curve (named "R07-#"). So the images cited above where plotted in the 1970s? <Jörg Yep, 180dpi Xerographic printer (UV crt discharges selenium cylinder). Same machine on which DEK developed TeX and Metafont. Zoom in. See the jaggies? But no developer beads. I was a good day. Those pages were cut from a roll *after* printing. (I wonder if the Computer History Museum has one.) Jörg>As an extra here is order 13 (there are 15 shapes), see http://jjj.de/tmp-rwg/search-r13-curves.txt Eyeballing http://jjj.de/tmp-rwg/all-r13-curve-decompositions.pdf should be enjoyable. <Jörg Hey, you could serialize these things as the L-System Technical Journal. (hardcopied in the 70s, pre-laser.) Also, did you notice this way of mis-teardropping the France fractal?gosper.org/jelly7.bmp Jörg>Never heard of the term "France fractal".<Jörg So what am I going to call it, the Smarandache Fractal? Dropping the left red part in http://gosper.org/jelly7.bmp gives "Gosper's island", right? If you insist.-) But note that's the gnarlier of two ways to do it. Trying to find the less gnarly, instead I found http://www.tweedledum.com/rwg/frac5Image4.gif and http://www.tweedledum.com/rwg/frac5Image2.gif . Ah, here it is: http://www.tweedledum.com/rwg/tear7Image4.gif --rwg Lastly, I had forgotten about these two teardroppings of Mandelbrot's seven Snowflake recursion:gosper.org/trozeImage8.gifgosper.org/trozeImage13.gif Jörg>Neat! Maybe someone can do his thirteen, but I can't do it in my head. I just found this: http://www.meden.demon.co.uk/Fractals/frozenteardrop.html . Yes, I know this one. Sadly, the recipes are (as almost always) left in the dark. Btw. many of the images given are the generalization of the unit square with complex numeration systems (such as the Heighway dragon with radix -1+i and digits 0 and 1). Best, jj Jörg> [...]