circular infinity
- From: "Eepē" <eepNOSPAM@xxxxxxxx>
- Date: Wed, 13 Dec 2006 07:11:21 GMT
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[
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;
]
But it only ever renders a single outer circle. :/
This fails with many errors:
cx = 0;
cy = 0;
r = 1;
SingleCircle = Show[
Graphics[
Circle[{cx, cy}, r]
], AspectRatio -> Automatic];
while[r > 1/(1/16),
cx=0 + r/2;
r = r/2;
SingleCircle[{cx, 0}, r];
cx = 0 - r/2\;
SingleCircle[{cx, 0}, r];
]
Any help would be appreciated. Thanks.
.
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