Unless I am confused, the orders of "paperfold and company" are powers of two. Indeed all of them can be obtained from the paperfolding curve by using the products I described in my pre-print. The paperfolding figures (plural) are instances of Dekking's "folding morphisms" ("Paperfolding morphisms, planefilling curves, and fractal tiles", Theoretical Computer Science, 2012). Not long ago I realized that I should be able to extend my search (at least on the square grid) to find _all_ of them for small orders. For the square grid I could so far only find curves for odd orders because my "simple L-systems" are more restrictive. I plan to do the search as soon as I find time (currently looking for some funding, wish me luck...). Best regards, jj P.S.: another plan is to go for "all Gosper curves", but this is unlikely to happen soon. * Bill Gosper <billgosper@gmail.com> [Dec 04. 2016 09:53]:
(This Subject is by now completely wrong. Dragons are related to base i-1, digits 0,1.)
It seems to me there should be 4 rep4tile "dragons": gosper.org/4flopfour.png , the Heighway and grid 2tiles, because they're also 4tiles, and one other proper 4tile. But my obvious guess makes gosper.org/bogus4tile.png which is not a rep4, maybe not a rep-anything. Jörg, what's the other rep4? Any idea what I blew to make this bogon --rwg
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