Is there a nice algorithm for adding two complex numbers via their expansions in this base, using some sort of carrying process? Jim Propp On Sunday, April 22, 2018, Bill Gosper <billgosper@gmail.com> wrote:
When the digits are 0 and 1 and the other two cuberoots of 1. See gosper.org/gaskettalk.pdf pp 11 and 13. E.g., i/√3 = red.cyangreencyangreencyangreen... = cyan.greenmagentagreenmagentagreen... . Presumably we can expect a lot of these multiple representations when the unit patch has a fractal boundary. PUZZLE: Here of dimension what? We need |base|² digits to cover a positive area in the complex plane. The "France fractal" bounds the unit patch of the base 2+i^(2/3) with digits zero and the 6th roots of 1. |2+i^(2/3)| = √7. Base 2+i^(2/3) with three digits moved outward gosper.org/base2+w.bmp has a unit patch with a boundary of large dimension. (PUZZLE: D=?) --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun