After Hilbert's N=2 and Wunderlich's N=3, every rule is the rule for N-2, with an extra two right angle turns concatenated on the end. I found the general construction procedure inductively, by studying the first few cases: https://0x0.st/zvIm.png ( blue / green triangles correspond to L / R symbols, arrows to F ) These curves have been drawn before, but I didn't look at the details. During a background search, Google revealed another oddity, which I had never seen or thought of: http://bl.ocks.org/nitaku/dcce9b645783d5239a04 Don't know if anyone has tried to answer the question of counting all possible Z^2 space-filling curves with NxN replacement grid, but it should be possible at least by brute force enumeration. --Brad On Mon, Sep 30, 2019 at 9:37 AM Joerg Arndt <arndt@jjj.de> wrote:
Nice pic(s), but I cannot decode the method!
Best regards, jj