Even "Peano's curve" isn't unique: Walter Wunderlich: {\"{U}ber Peano-Kurven}, Elemente der Mathematik, vol.~28, no.~1, pp.~1-10, (1973). http://sodwana.uni-ak.ac.at/geom/mitarbeiter/wallner/wunderlich/ Don't let the German scare you, just check the images. For the n-dimensional version of (one of) the Peano curve(s): https://jjj.de/fxt/demo/comb/index.html#peano-ndim This is following A.\ J.\ Cole: {A note on space filling curves}, Software Practice and Experience, vol.~13, no.~12, (1983) and A.\ J.\ Cole: {A Note on Peano Polygons and Gray Codes}, International Journal of Computer Mathematics, vol.~18, no.~1, pp.~3-13, (1985). These papers win both my "horrible notation" and "most useless example" award. Best regards, jj P.S. regarding Peanistic curves: https://jjj.de/tmp-math-fun/all-R29-curves.pdf https://jjj.de/tmp-math-fun/all-R29-tiles.pdf View both files side-by-side. * Bill Gosper <billgosper@gmail.com> [Sep 20. 2019 10:10]:
For decades I misapprehended Hilbert's spacefill as Peano's. Today at last, I corrected my web page: http://www.tweedledum.com/rwg/samhilbert.htm . The impetus was discovering that my blunder has been copied onto other websites. Unfortunately, with correct attribution.-} —rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun