Re: circular infinity

*To*: mathgroup at smc.vnet.net*Subject*: [mg72189] Re: circular infinity*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Thu, 14 Dec 2006 05:49:03 -0500 (EST)*Organization*: The Open University, Milton Keynes, UK*References*: <elotg7$pe2$1@smc.vnet.net>

Eep² wrote: > "Jean-Marc Gulliet" <jeanmarc.gulliet at gmail.com> wrote in message news:12nvcd7lp01bte8 at corp.supernews.com... >> Eep² wrote: >>> Hi, I'm trying to create the image at http://tnlc.com/eep/circles.html in Mathematica but I don't have much programming (or math) experience and am wondering if anyone here could help me out. I tried posting in comp.soft-sys.math.mathematica but it's moderated and my posts STILL haven't shown up in days. Here's what I have so far: >>> >>> Manual: >>> >>> Show[Graphics[{ >>> Circle[{0, 0}, 2], >>> >>> Circle[{-1, 0}, 1], Circle[{1, 0}, 1], >>> >>> Circle[{-1.5, 0}, .5], Circle[{1.5, 0}, .5], >>> Circle[{-.5, 0}, .5], Circle[{.5, 0}, .5], >>> >>> Circle[{-1.75, 0}, .25], Circle[{-1.25, 0}, .25], >>> Circle[{-.75, 0}, .25], Circle[{-.25, 0}, .25], Circle[{.25, 0}, .25], >>> Circle[{.75, 0}, .25], Circle[{1.25, 0}, .25], Circle[{1.75, 0}, .25], >>> >>> Circle[{-1.875, 0}, .125], Circle[{-1.625, 0}, .125], >>> Circle[{-1.375, 0}, .125], Circle[{-1.125, 0}, .125], >>> Circle[{-.875, 0}, .125], Circle[{-.625, 0}, .125], >>> Circle[{-.3725, 0}, .125], Circle[{-.125, 0}, .125], >>> Circle[{.375, 0}, .125], Circle[{.625, 0}, .125], >>> Circle[{.875, 0}, .125], Circle[{.125, 0}, .125], >>> Circle[{1.125, 0}, .125], Circle[{1.375, 0}, .125], >>> Circle[{1.625, 0}, .125], Circle[{1.875, 0}, .125], >>> >>> Circle[{-1.9375, 0}, .0625], Circle[{-1.8125, 0}, .0625], >>> Circle[{-1.6875, 0}, .0625], Circle[{-1.5675, 0}, .0625], >>> Circle[{-.875, 0}, .0625], Circle[{-.625, 0}, .0625], >>> Circle[{-.3725, 0}, .0625], Circle[{-.125, 0}, .0625], >>> Circle[{.375, 0}, .0625], Circle[{.625, 0}, .0625], >>> Circle[{.875, 0}, .0625], Circle[{.125, 0}, .0625], >>> Circle[{1.5675, 0}, .0625], Circle[{1.6875, 0}, .0625], >>> Circle[{1.8125, 0}, .0625], Circle[{1.9375, 0}, .0625] >>> }], AspectRatio -> Automatic] >>> >>> The last iteration needs spacing work still--I just got tired of writing it out manually... >>> >>> Based off the formula on http://local.wasp.uwa.edu.au/~pbourke/fractals/circles/ for POV-Ray: >>> >>> cx = 0; >>> cy = 0; >>> r = 1; >>> >>> SingleCircle = Show[ >> --------------^^ >> You have not defined a function: the parameters list is missing. >> Also, you should use := (SetDelayed). >> >>> Graphics[ >>> Circle[{cx, cy}, r] >>> ] >>> , AspectRatio -> Automatic >>> ]; >>> >>> loopradius = 1; >>> nn = 1; >>> iterations = 1; >>> >>> While [ >>> (iterations < 8), >>> loopradius = loopradius/2; >>> nn = 2*nn; >>> n = -(nn - 1); >>> >>> While[n <= nn - 1, >>> SingleCircle[{-n/nn, 0}, loopradius]; >>> n = n + 2; >>> ] >> -----------^ >> A semi column marking the end of the inner loop is missing. >> >>> iterations = iterations + 1; >>> ] >>> >>> But it only ever renders a single outer circle. :/ >>> >>> This fails with many errors: >> So you could start with, >> >> cx = 0; >> cy = 0; >> r = 1; >> >> SingleCircle[{cx_, cy_}, r_] := >> Show[Graphics[Circle[{cx, cy}, r]], AspectRatio -> Automatic]; >> >> loopradius = 1; >> nn = 1; >> iterations = 1; >> >> While[iterations < 8, >> loopradius = loopradius/2; >> nn = 2*nn; >> n = -(nn - 1); >> While[n <= nn - 1, >> SingleCircle[{-n/nn, 0}, loopradius]; >> n = n + 2; >> ]; >> iterations = iterations + 1; >> ] > > Thanks for the corrections but this gives the error: > SetDelayed::write: Tag Graphics in (-Graphics-)[{cx_, cy_}, r_] is Protected. > >>> cx = 0; >>> cy = 0; >>> r = 1; >>> >>> SingleCircle = Show[ >> --------------^^ >> You have not defined a function: the parameters list is missing. >> Also, you should use := (SetDelayed). >> >>> Graphics[ >>> Circle[{cx, cy}, r] >>> ], AspectRatio -> Automatic]; >>> >>> while[r > 1/(1/16), >> --^ --------^^^^^^^^ >> Mathematica function names are *always* capitalized. >> Moreover, you test r greater than 16, so you'll never enter the loop. >> >>> cx=0 + r/2; >>> r = r/2; >>> SingleCircle[{cx, 0}, r]; >>> cx = 0 - r/2\; >> ------------------^ >> Wrong place for a backslah here. > > Left in from having to edit out all of Mathematica's code after pasting... > >>> SingleCircle[{cx, 0}, r]; >>> ] >> The following expressions will give you better results although not yet what you are looking for: >> >> cx = 0; >> cy = 0; >> r = 1; >> >> SingleCircle[{cx_, cr_}, r_] := >> Show[Graphics[Circle[{cx, cy}, r]], AspectRatio -> Automatic]; >> >> While[r > 1/16, cx = 0 + r/2; >> r = r/2; >> SingleCircle[{cx, 0}, r]; >> cx = 0 - r/2; >> SingleCircle[{cx, 0}, r]; ] > > This also gives the same error as above. > Try to run the code in a new Mathematica session. Both given expression works fine on my system. (They produce several graphics showing circles.) No warning nor error messages are displayed. In[1]:= cx = 0; cy = 0; r = 1; SingleCircle[{cx_, cy_}, r_] := Show[Graphics[Circle[{cx, cy}, r]], AspectRatio -> Automatic]; loopradius = 1; nn = 1; iterations = 1; While[iterations < 8, loopradius = loopradius/2; nn = 2*nn; n = -(nn - 1); While[n <= nn - 1, SingleCircle[{-n/nn, 0}, loopradius]; n = n + 2; ]; iterations = iterations + 1; ] In[9]:= cx = 0; cy = 0; r = 1; SingleCircle[{cx_, cr_}, r_] := Show[Graphics[Circle[{cx, cy}, r]], AspectRatio -> Automatic]; While[r > 1/16, cx = 0 + r/2; r = r/2; SingleCircle[{cx, 0}, r]; cx = 0 - r/2; SingleCircle[{cx, 0}, r]; ] In[14]:= $Version Out[14]= "5.2 for Microsoft Windows (June 20, 2005)" Regards, Jean-Marc