Neat animation! Why did you make the "seeds" get bigger with radius? By the way, my calculator says the angle is 137.507764... And thank you for this post. I had long ago written some PostScript to produce the sunflower graphic, but for large values of n it produced unexpected (i.e., wrong) results due to PS reals being single precision in most implementations (including ghostscript), coupled with my naive multiplication of the magic angle by the loop index. It didn't occur to me to just use PostScript's internal CTM mechanism, which is double-precision in ghostscript and presumably other implementations, to do the rotation part of "seed" positioning. I'm embarrassed to say it didn't even occur to me to do a simple fixed point multiplication to preserve precision when multiplying the magic angle. For what it's worth, this is my corrected PS: %!PS-Adobe-3.0 % Replace just the first occurrence of 2048 by the desired n, or, in interactive mode, % type "/n 100000 def" before running the file to produce 100000 seeds. % Scaling is done automatically to keep the entire graphic centered on a letter-sized page. /default {1 index where {pop pop pop} {def} ifelse} bind readonly def /n 2048 default /s 5 n 2048 div sqrt div def currentpagedevice /PageSize get aload pop .5 mul exch .5 mul exch translate s s scale 1 setlinewidth 1 setlinecap /360phinv -137.50776405003785464634873962837 def /pt {sqrt 0} readonly bind def 1 1 n {360phinv rotate pt moveto closepath stroke} for showpage On 3/22/2012 10:24 PM, Stuart Anderson wrote:
The following small postscript program provides a similar graphic;
%!PS 297 421 translate 0 .1 400{dup dup sqrt 4 div 0 360 arc fill 137.50775 rotate}for showpage
137.50775.. is the 'golden angle'
If you gradually change the rotation angle and animate , you get this;
http://www.youtube.com/watch?v=1GK1JfivJSU
No editing was done, just a gradual change of angle. what interested me was the appearance and metamorphosis of different cycles.
Stuart _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun