On Thu, Mar 19, 2020 at 5:40 PM Bill Gosper <billgosper@gmail.com> wrote:
I was chagrinned to realize that the popularity of this curve is probably due to how carefully it self-avoids when you sample it at the natural frequencies of 7^n. Ironically, like all true spacefillers, it's actually dense with triple points:
In[299]:= unflow[3/7 + I/7/\[Sqrt]3]
Out[299]= {5/42, 11/42, 17/42}
In[296]:= FlowS /@ {5/42, 11/42, 17/42}
Out[296]= {3/7 + I/(7 Sqrt[3]), 3/7 + I/(7 Sqrt[3]), 3/7 + I/(7 Sqrt[3])}
In[300]:= unflow[223/686 - (19 I)/(686 Sqrt[3])]
Out[300]= {257/2058, 263/2058, 281/2058}
In[297]:= FlowS /@ {257/2058, 263/2058, 281/2058}
Out[297]= {223/686 - (19 I)/(686 Sqrt[3]), 223/686 - (19 I)/(686 Sqrt[3]), 223/686 - (19 I)/(686 Sqrt[3])}
(Without Julian bailing me out!) I finally found a bug that was driving me nuts. flowsnake triple points of the form n/6/7/7/7 <http://gosper.org/flotrips2.png> I believe all the triple points are of the form n/6/7^k. —rwg