What about thirds and sevenths? Is this dragon-subdivision all old news? On Thu, Nov 17, 2011 at 6:00 AM, Bill Gosper <billgosper@gmail.com> wrote:
In[135]:= $RecursionLimit = 9999; Clear[Drag]; Drag[t_, a1_: 1, a0_: 0] := Drag[t, b1_: 1, b0_: 0] = (Drag[t, s1_: 1, s0_: 0] = ((a0 - s0)/(s1 - a1)); Module[{t2 = 2*t, n}, n = Floor[t2]; t2 -= n; Switch[n, 0, (I + 1)/2*Drag[t2, a1*(I + 1)/2, a0], 1, 1 + (I - 1)/2*Drag[1 - t2, (I - 1)/2*a1, a1 + a0], 2, 1]]) E.g., In[136]:= Drag[7/22]
Out[136]= 23/82 + 39 I/82
In[137]:= % - Drag[113/355]
Out[137]= 517517964757026532787/96808512898827726880686 + 650828352727980554837 I/96808512898827726880686
In[138]:= N[%]
Out[138]= 0.00534579 + 0.00672284 I (The Dragon function is continuous.)
Dividing the domain [0,1] into equal fifths, ListLinePlot[ Partition[Table[{Re@#, Im@#} &@Drag[t/4/2048], {t, 8190}],1638], AspectRatio -> Automatic, Axes -> None]
may surprise you: http://gosper.org/dragon5ths.png
The obligatory continuous texture drift: ListLinePlot[Table[{Re@#, Im@#} &@Drag[t], {t, 0, 1, 1/513}], AspectRatio -> Automatic, Axes -> None]
and ListLinePlot[Table[{Re@#, Im@#} &@Drag[t], {t, 1/1024, 1, 1/513}], AspectRatio -> Automatic, Axes -> None]
http://gosper.org/driftdrags.png --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun