)mw2.0 Englishprojectsize[744 426]turtles-have[]globals[]globals-list[globals-vars] shapesprocedurestext{\rtf1\ansi\ansicpg1252\deff0\deflang3081{\fonttbl{\f0\fmodern\fprq1\fcharset0 Courier New;}} {\colortbl ;\red0\green128\blue128;\red0\green0\blue255;} \viewkind4\uc1\pard\cf1\f0\fs20 ; Fractal dreams \par \par ; by Dr Clifford Pickover \par \par \par ; The book Chaos in Wonderland just came out in paperback, and I thought ; some of you would like a computer recipe from the book. The book is a ; blend of science fiction, graphics, mathematics, astronomy, computer ; ; graphics, and fractals to introduce the reader to chaos science -- the ; science behind many intricate, unpredictable patterns in mathematics ; ; and nature. \par \par \par ; In the book, status in the alien's society is based on the beauty of ; their fractal dreams. The following steps are required to create the \par ; swirling patterns: \par \par \par ; http://www.geocities.com/CapeCanaveral/Launchpad/5113/fr40.htm \par \par ; x = 0.1; y = 0.1; /* starting point */ \par ; DO 10 Million Times \par ; xnew = sin(y*b) + c*sin(x*b) \par ; ynew = sin(x*a) + d*sin(y*a) \par ; x = xnew; y = ynew; PlotDotAt (x, y) \par ; END \par \par ; The values of the real number constants a, b, c, and d may be chosen \par ; at random in a range (-3 < a,b < 3) and (0.5 < c, d < 1.5 ). \par \par ; (a = -0.966918, b = 2.879879, c = 0.765145, and d = 0.744728). \par ; The picture boundaries are (-1.86 < x < 1.86) and (-1.51 < y < 1.51) . \par \cf0 \par \cf2\b to dream\cf0\b0 \par cg \par cc \par pu \par ht \par make "x 0.1 \par make "y 0.1 \par \par make "a -0.966918 \par make "b 2.879879 \par make "c 0.765145 \par make "d 0.744728 \par \par make "scale 200 \par \par repeat 100000 [ \par make "xnew sin(:y * :b) + :c * sin (:x * :b) \par make "ynew sin(:x * :a) + :d * sin(:y * :a) \par make "x :xnew * :scale \par make "y :ynew * :scale \par \par setx :x \par sety :y \par \par pd \par fd 0\tab\tab\tab\cf1 ; draw a point without moving the turtle \par \cf0 pu \par ] \par \par \cf2\b end\cf0\b0 \par \par \par } %pagenamepage1curturtlet1curtext||transition0Dturtle-deamons[[] [] [] [] [] [] [] [] [] [] [] [] [] [] [] []]Cmouse-deamons[[] [] [] [] [] [] [] [] [] [] [] [] [] [] [] []]bg0Tbuffer=$6HZl~?, T 75i?]d "{$&y({*Y,x.g0A24679;=?ACEqG]I+KMOPR{TOVXY[&]_ abdfh;j%lmoqcs!uvxz_| ~Iu Ց)#^0ȩtDr5κv-zpTu8}SKf|cO   pZaE"!)# %R'L)R+P-q/1358<:_<>@BDFHHKDMgOoQSUWY[]3`fbdfh kmo8qfs?umwqy{}Ɓ׃ڇ   <=CVucrߪ!!nqw{rfY7/(%z. x!o7Y[;  h+#e3T. !#G%5'(*n,./13X5 78:j<">?AKC-EFBHJKMO`QRSUVX7Z\]_afcCeghjlFnoq;stvxQz|~pɆu%яsP:ݚoL<ǭXM1 ׸speU5o RZ);M_q             object typet namet1locked?falsexpos358.628579ypos25.7445994418 shape0penstate0 size40pencolor0 heading0 pensize1shown?falsefcn[dream] kind1shapeinturtlehave-list[has] colorin9~objecttypebuttonnamebutton1rect[7 368 60 25]show-name?falselocked?falsefcn[clean] kind1~objecttypebuttonnamebutton2rect[6 397 60 25]show-name?falselocked?falsefcn[dream] kind1