For Triangle space-filler, another neat example, see also [1]. It is not 2x2 per se, but has the same inflation factor, as does half-hex substitution system [1]. It is possible to make many half-hex space fillers using at most 4 symbols in 4 reflection classes. I don't think this area has been explored yet. It looks like JZH's PRF function is easier to call when the replacement has one or two symbols, but input arguments become cumbersome when adding so many rules (cf. [1] "trifil25"). JZH probably does have the helper functions for producing arguments from, say, Lindenmayer rules, but documentation so far is scarce. Does he plan to write up a paper, user manual, or demonstration? Here are a few more objectives, not too difficult: * Complete Q-functions for 96 2x2 Z-functions on four letters and compare multi-points. More "functional equations" / identities / addition rules? * Calculate Z functions for half-hex substitution system (too many to count?). * Analysis of Z-function scrambles such as [3]? When is the output easy or difficult to understand? --Brad [1] https://community.wolfram.com/groups/-/m/t/912279 [2] https://tilings.math.uni-bielefeld.de/substitution/half-hex/ ( and also: https://tilings.math.uni-bielefeld.de/substitution/hexagonal-aperiodic-monot... ) [3] https://www.youtube.com/watch?v=Wdd9JFD_N0c (blame youtube encoding for blurry vid. argggg.) On Wed, Oct 9, 2019 at 12:00 PM Bill Gosper <billgosper@gmail.com> wrote:
Oh, to be young again.