Since geeky science questions seem to be today's fashion...
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OK, I understood your concoction as a two-dimensional drawing where you have N "top-connected" circles of decreasing diameter (with N increasing without bound), and you travel to the next circle every time you reach the top, until you reached the smallest one, then you step to the outer one again. So that is a closed line, there is nothing to zoom that would keep the overall impression, and the area is a half circle. Not a fractal. If you want to visualize it as a spiral, i.e. each next circle moves you a bit in the third dimension, then you have somewhat of a fractal effect as you can move forward over the pitch of the spiral, and zoom in a bit to compensate for the decreasing diameter. But now it is just a spiral, it spans an infinite z-axis. So it is not contained in a finite space. (In fact it resembles a worm hole in Stargate-1). All my senses and I agree yours is not a space-limited fractal, and not the right answer to the OP. But I agree you might still like it as a wall paper. You, not me. :laugh: This[^] might offer some consolation.
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Luc Pattyn wrote:
OK, I understood your concoction as a two-dimensional drawing where you have N "top-connected" circles of decreasing diameter (with N increasing without bound), and you travel to the next circle every time you reach the top
Yep.
Luc Pattyn wrote:
until you reached the smallest one, then you step to the outer one again
There is no "smallest" one. It keeps going, forever.
Luc Pattyn wrote:
there is nothing to zoom that would keep the overall impression
I used my excellent skills as an artist to make this rendition of what I was thinking. Suppose you started out zoomed to view the full shape. Then, you zoom so that you can only view the part of the shape composed of light grey circles. Then you keep zooming in that fashion. You'll always see circles within circles, all intersecting at the top of the view. It is this self-similarity that I used to define this as a fractal.
Luc Pattyn wrote:
not the right answer to the OP
Nonsense!
Luc Pattyn wrote:
This[^] might offer some consolation.
Sorry it took so long to respond... I just woke up from a seizure induced by that crazy image. ;P
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Luc Pattyn wrote:
OK, I understood your concoction as a two-dimensional drawing where you have N "top-connected" circles of decreasing diameter (with N increasing without bound), and you travel to the next circle every time you reach the top
Yep.
Luc Pattyn wrote:
until you reached the smallest one, then you step to the outer one again
There is no "smallest" one. It keeps going, forever.
Luc Pattyn wrote:
there is nothing to zoom that would keep the overall impression
I used my excellent skills as an artist to make this rendition of what I was thinking. Suppose you started out zoomed to view the full shape. Then, you zoom so that you can only view the part of the shape composed of light grey circles. Then you keep zooming in that fashion. You'll always see circles within circles, all intersecting at the top of the view. It is this self-similarity that I used to define this as a fractal.
Luc Pattyn wrote:
not the right answer to the OP
Nonsense!
Luc Pattyn wrote:
This[^] might offer some consolation.
Sorry it took so long to respond... I just woke up from a seizure induced by that crazy image. ;P
aspdotnetdev wrote:
I just woke up from a seizure induced by that crazy image
And you make even more sense than before. Yes, I stand corrected, your 2D image has some fractal behavior; it is a bit special as it seems to require one looks through a circular hole; that way you can hide the larger circles entirely while zooming in, something a square view fails to do for moderate zoom levels. The area problem remains; the odd/even rule still seems to lead to a half circle area. What does Gregory say on the subject? PS: excellent artistic skills indeed; why didn't you fill the interior to settle the area issue too? :)
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aspdotnetdev wrote:
I just woke up from a seizure induced by that crazy image
And you make even more sense than before. Yes, I stand corrected, your 2D image has some fractal behavior; it is a bit special as it seems to require one looks through a circular hole; that way you can hide the larger circles entirely while zooming in, something a square view fails to do for moderate zoom levels. The area problem remains; the odd/even rule still seems to lead to a half circle area. What does Gregory say on the subject? PS: excellent artistic skills indeed; why didn't you fill the interior to settle the area issue too? :)
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Luc Pattyn wrote:
the odd/even rule
Luc Pattyn wrote:
half circle area
Luc Pattyn wrote:
fill the interior to settle the area issue
Still no idea what you are talking about there. It is an infinitely thin/long string wrapped in a bunch of circles (perhaps "loops" would be a better term, as the "circles" aren't filled in). There's no surface, so there's no area! You'll send me to the looney bin, you will.
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In terms of area, remember that
null != 0;:laugh:Gregory.Gadow wrote:
In terms of area, remember that null != 0;
which metric? ha! Infinite length of edges, zero area and covers an n-dimensional volume. For an added bonus it's used to show that n-intervals have the same cardinality as the 1-interval. What's not to love? Your fractal only has an area that tends to zero, mine has zero volume before the limit :)
I can imagine the sinking feeling one would have after ordering my book, only to find a laughably ridiculous theory with demented logic once the book arrives - Mark McCutcheon
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That would be a fractal, such as this Sierpinski triangle[^]. ADDED Although not many would agree they have 2 or 3 (or any integer) number of dimensions... :)
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modified on Thursday, May 6, 2010 6:06 PM
My fractal has less area than yours. neener neener neener.
I can imagine the sinking feeling one would have after ordering my book, only to find a laughably ridiculous theory with demented logic once the book arrives - Mark McCutcheon
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Luc Pattyn wrote:
the odd/even rule
Luc Pattyn wrote:
half circle area
Luc Pattyn wrote:
fill the interior to settle the area issue
Still no idea what you are talking about there. It is an infinitely thin/long string wrapped in a bunch of circles (perhaps "loops" would be a better term, as the "circles" aren't filled in). There's no surface, so there's no area! You'll send me to the looney bin, you will.
So now it is a spiral in 2D, it no longer is a collection of circles. Just an infinite line, curled rather than straight? That's a bit disappointing...
aspdotnetdev wrote:
You'll send me to the looney bin, you will.
We could organize a geeky science home party then. :laugh:
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In terms of area, remember that
null != 0;:laugh:Gregory.Gadow wrote:
null != 0;
in my world, that does not even compile. :)
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My fractal has less area than yours. neener neener neener.
I can imagine the sinking feeling one would have after ordering my book, only to find a laughably ridiculous theory with demented logic once the book arrives - Mark McCutcheon
maybe your fractal is broken? :)
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Luc Pattyn wrote:
the odd/even rule
Luc Pattyn wrote:
half circle area
Luc Pattyn wrote:
fill the interior to settle the area issue
Still no idea what you are talking about there. It is an infinitely thin/long string wrapped in a bunch of circles (perhaps "loops" would be a better term, as the "circles" aren't filled in). There's no surface, so there's no area! You'll send me to the looney bin, you will.
It doesn't actually fill a volume unless you choose your radii carefully. For example if you pick r(i) = (1/2)i than you have finite sized gaps between each of the circles. You'd have to pick something like 1, 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, ... so that it ended up filling the whole circle. Also without specifying the way that the radii decrease, you could end up with a finite length as opposed to an infinite one.
I can imagine the sinking feeling one would have after ordering my book, only to find a laughably ridiculous theory with demented logic once the book arrives - Mark McCutcheon
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maybe your fractal is broken? :)
Luc Pattyn [Forum Guidelines] [Why QA sucks] [My Articles]
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:rolleyes:
I can imagine the sinking feeling one would have after ordering my book, only to find a laughably ridiculous theory with demented logic once the book arrives - Mark McCutcheon
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So now it is a spiral in 2D, it no longer is a collection of circles. Just an infinite line, curled rather than straight? That's a bit disappointing...
aspdotnetdev wrote:
You'll send me to the looney bin, you will.
We could organize a geeky science home party then. :laugh:
Luc Pattyn [Forum Guidelines] [Why QA sucks] [My Articles]
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Luc Pattyn wrote:
So now it is a spiral in 2D, it no longer is a collection of circles. Just an infinite line, curled rather than straight? That's a bit disappointing...
I'm glad we finally understand eachother. :rolleyes:
Luc Pattyn wrote:
We could organize a geeky science home party then.
I hear Weven is hosting these promotion parties. Yay, sounds like fun! ;P
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It doesn't actually fill a volume unless you choose your radii carefully. For example if you pick r(i) = (1/2)i than you have finite sized gaps between each of the circles. You'd have to pick something like 1, 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, ... so that it ended up filling the whole circle. Also without specifying the way that the radii decrease, you could end up with a finite length as opposed to an infinite one.
I can imagine the sinking feeling one would have after ordering my book, only to find a laughably ridiculous theory with demented logic once the book arrives - Mark McCutcheon
How about we say the distance the from the outer circle is a function of the angle. How about:
radius = 100 - 1/(1 + 1/(angle! + googleplex * ackerman(angle, angle)))
That ought to work. :rolleyes:
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How about we say the distance the from the outer circle is a function of the angle. How about:
radius = 100 - 1/(1 + 1/(angle! + googleplex * ackerman(angle, angle)))
That ought to work. :rolleyes:
That's even worse! It converges even more quickly to a single point, leaving gaps over most of the circle and it most definitely has finite length.
I can imagine the sinking feeling one would have after ordering my book, only to find a laughably ridiculous theory with demented logic once the book arrives - Mark McCutcheon
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How about we say the distance the from the outer circle is a function of the angle. How about:
radius = 100 - 1/(1 + 1/(angle! + googleplex * ackerman(angle, angle)))
That ought to work. :rolleyes:
The links in your post are broken: **http://www.codeproject.com/script/Forums/**"http://en.wikipedia.org/wiki/Ackermann\_function" Did you do this intentionally or did you find a new CP bug?
3x12=36 2x12=24 1x12=12 0x12=18
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The links in your post are broken: **http://www.codeproject.com/script/Forums/**"http://en.wikipedia.org/wiki/Ackermann\_function" Did you do this intentionally or did you find a new CP bug?
3x12=36 2x12=24 1x12=12 0x12=18
Gotta be a CP bug. Here is the text I see when I edit my post:
My post:
How about we say the distance the from the outer circle is a function of the angle. How about: <pre lang="text">radius = 100 - 1/(1 + 1/(angle! + <a href="http://en.wikipedia.org/wiki/Googleplex">googleplex</a> * <a href="http://en.wikipedia.org/wiki/Ackermann\_function">ackerman</a>(angle, angle)))</pre> That ought to work. :rolleyes:
Could be because I put the links in a PRE tag. Let me test that: Not in a PRE tag.
EDIT: Correct placement of blockquote start tag.
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The links in your post are broken: **http://www.codeproject.com/script/Forums/**"http://en.wikipedia.org/wiki/Ackermann\_function" Did you do this intentionally or did you find a new CP bug?
3x12=36 2x12=24 1x12=12 0x12=18
Yep, looks like the bug occurs when a link is placed in a PRE tag. I'll let you have the honors of reporting that one. :)
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That's even worse! It converges even more quickly to a single point, leaving gaps over most of the circle and it most definitely has finite length.
I can imagine the sinking feeling one would have after ordering my book, only to find a laughably ridiculous theory with demented logic once the book arrives - Mark McCutcheon
Nope. Let's go through it.
angle! + googleplex * ackerman(angle, angle)
Assuming you start at 1 for the angle, the result is a very rapidly growing number. Let's call this "growingNumber" for short. So the equation becomes:
100 - 1/(1 + 1/growingNumber)
Now, what happens when you divide 1 by a growing number:
1/growingNumber
You get a number that decreases in magnitude as the input increases. Since "growingNumber" starts out very large (at least a googleplex), that means this "shrinkingNumber" starts out extremely small (no larger than 1/googleplex), and only gets closer to 0 (but never reaches 0). So the equation becomes:
100 - 1/(1 + shrinkingNumber)
That portion in parens starts out as something like 1.0000001 (only with many more 0's) and keeps getting smaller, but never goes below 1 (because shrinkingNumber never goes below 0). So, the firt result looks something like:
100 - 1/1.000001
And a later result looks like:
100 - 1/1.0000000000000000000000000000000001
That first result would be something like 99.0000000001. And the later result would be something like 99.000000000000000000000000000001. The number gets smaller, but never below 99. So the circle goes forever, always with a radius between 100 and 99. Sure, it leaves 98 to 0 empty, but that doesn't make it any less infinite. :)
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Q: Describe a 2 or 3 dimensional shape with an infinite edge and zero area, which takes up a finite amount of space.
How about a three dimensional figure that has an edge, but only one edge, and has only one surface, and encloses a volume?
