* Bill Gosper <billgosper@gmail.com> [Nov 21. 2016 10:12]:
[...]
Even unto the lowly dyadic (Heighway)
dragon which, if you conjugate at every level, becomes simply a triangular patch of a square grid. Two back-to-back: gosper.org/dragrid199.png --rwg Is there a gallery of variously flopped dragons anywhere?
Jörg?
See http://jjj.de/fxt/demo/bits/#bit-paper-fold-general for "all" variations (for 2^64 \approx \infty). Crucially: static inline bool bit_paper_fold_general(ulong k, ulong w) // Return element number k of the general paper-folding sequence: // bit number x of the words w determines whether // a left or right fold is made at the step x. // With w==0 the result is ! bit_paper_fold(k). // With w==~0 the result is bit_paper_fold(k). // The result with ~w is the complement of the result with w. { ulong h = k & -k; // == lowest_one(k) h <<= 1; ulong t = h & (k^w); return ( t!=0 ); } For edge-covering curves on the grids (3^6), (4^4), and (3.6.3.6) there is http://jjj.de/3frac/ Dive into the directories p?/ (for ? \in {3,4,6}) for pdfs But these are only curves with simple L-systems. By the way, I am preparing high quality prints (poster size), two of which will be shown in Atlanta in January, see http://gallery.bridgesmathart.org/exhibitions/2017-joint-mathematics-meeting... Will any math-funster be there? I have yet to do all "paper-folding" curves a la Davis/Knuth/Dekking for other orders. It's not hard, but I have been working on other things.
Julian, can they be made with piecewiserecursivefractal?
No, but by another function in his same notebook! --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun