What it *looks* like is that there is a small range of angles just short of pi/2, the curve self-crosses. Prove to me that this is *not* happening on a microscopic scale for angles short of that small range. On Fri, Dec 22, 2017 at 5:14 PM, Bill Gosper <billgosper@gmail.com> wrote:

Sounds familiar--I probably heard and forgot. Somebody probably even knows the minimal D. gosper.org/drinkle3.gif --rwg (Picture credit: Julian's software.) _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

On Fri, Dec 22, 2017 at 2:14 PM, Bill Gosper <billgosper@gmail.com> wrote:

Sounds familiar--I probably heard and forgot. Somebody probably even knows the minimal D. gosper.org/drinkle5.gif --rwg (Picture credit: Julian's software.)

It looks like not-quite 2D triadic dragons barely avoid self crossing: [misleading gif deleted] gosper.org/trinkle3o6560.gif gosper.org/trinkle1458.gif Now it looks like they cross: gosper.org/tridragcrunch.png shows a segment completely inside a loop. Segments are not on the "curve", but their endpoints are, so these broken-line diagrams are useful after all.

In any case, the triadic dragon's interval(?) of collision dimensions is way smaller than the Heighway's.. --rwg