Re: [math-fun] Fractals are now recondite?
Mike Stay>That's great! May I suggest that when the area is smallest, you should give those three regions the labels 1, 2, and 3? Thanks! How's http://gosper.org/flaky.gif ? --rwg On Fri, Oct 4, 2013 at 2:41 AM, Bill Gosper <billgosper@gmail.com> wrote: Funster Gary Antonick (NYT NumberPlay) fears that the Franceflake fractal boundary paradox might be too hairy for his readers, even though Martin Gardner explained it in his original Flowsnake piece. So I made an mgif (gosper.org/flake.gif) illustrating the problem, and offering a URL for an (indirect) explanation. --rwg _______________________________________________ -- Mike Stay - metaweta@gmail.comhttp://www.cs.auckland.ac.nz/~mikehttp://reperiendi.wordpress.com _____________________________________________
Wonderful. On Fri, Oct 4, 2013 at 12:47 PM, Bill Gosper <billgosper@gmail.com> wrote:
Mike Stay>That's great! May I suggest that when the area is smallest, you should give those three regions the labels 1, 2, and 3?
Thanks! How's http://gosper.org/flaky.gif ?
--rwg
On Fri, Oct 4, 2013 at 2:41 AM, Bill Gosper <billgosper@gmail.com> wrote:
Funster Gary Antonick (NYT NumberPlay) fears that the Franceflake fractal boundary paradox might be too hairy for his readers, even though Martin Gardner explained it in his original Flowsnake piece. So I made an mgif (gosper.org/flake.gif) illustrating the problem, and offering a URL for an (indirect) explanation. --rwg _______________________________________________
-- Mike Stay - metaweta@gmail.comhttp://www.cs.auckland.ac.nz/~mikehttp://reperiendi.wordpress.com
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-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Oh, it just occurred to me that the URL in the image isn't selectable; you might want to replace that with something more easily typed involving tinyurl.com or goo.gl or whatever. On Fri, Oct 4, 2013 at 12:52 PM, Mike Stay <metaweta@gmail.com> wrote:
Wonderful.
On Fri, Oct 4, 2013 at 12:47 PM, Bill Gosper <billgosper@gmail.com> wrote:
Mike Stay>That's great! May I suggest that when the area is smallest, you should give those three regions the labels 1, 2, and 3?
Thanks! How's http://gosper.org/flaky.gif ?
--rwg
On Fri, Oct 4, 2013 at 2:41 AM, Bill Gosper <billgosper@gmail.com> wrote:
Funster Gary Antonick (NYT NumberPlay) fears that the Franceflake fractal boundary paradox might be too hairy for his readers, even though Martin Gardner explained it in his original Flowsnake piece. So I made an mgif (gosper.org/flake.gif) illustrating the problem, and offering a URL for an (indirect) explanation. --rwg _______________________________________________
-- Mike Stay - metaweta@gmail.comhttp://www.cs.auckland.ac.nz/~mikehttp://reperiendi.wordpress.com
_____________________________________________ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
That's a really cool demo! I wonder what the area is of the triangular figure of the map-of-France at the moment the 3 "segments" first touch. --Dan On 2013-10-04, at 11:47 AM, Bill Gosper wrote:
Mike Stay>That's great! May I suggest that when the area is smallest, you should give those three regions the labels 1, 2, and 3?
Thanks! How's http://gosper.org/flaky.gif ?
--rwg
On Fri, Oct 4, 2013 at 2:41 AM, Bill Gosper <billgosper@gmail.com> wrote:
Funster Gary Antonick (NYT NumberPlay) fears that the Franceflake fractal boundary paradox might be too hairy for his readers, even though Martin Gardner explained it in his original Flowsnake piece. So I made an mgif (gosper.org/flake.gif) illustrating the problem, and offering a URL for an (indirect) explanation. --rwg _______________________________________________
-- Mike Stay - metaweta@gmail.comhttp://www.cs.auckland.ac.nz/~mikehttp://reperiendi.wordpress.com
_____________________________________________ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Guess: It's 1/21 of the large figure. --Dan On 2013-10-04, at 1:27 PM, Dan Asimov wrote:
That's a really cool demo!
I wonder what the area is of the triangular figure of the map-of-France at the moment the 3 "segments" first touch.
--Dan
On 2013-10-04, at 11:47 AM, Bill Gosper wrote:
Mike Stay>That's great! May I suggest that when the area is smallest, you should give those three regions the labels 1, 2, and 3?
Thanks! How's http://gosper.org/flaky.gif ?
--rwg
On Fri, Oct 4, 2013 at 2:41 AM, Bill Gosper <billgosper@gmail.com> wrote:
Funster Gary Antonick (NYT NumberPlay) fears that the Franceflake fractal boundary paradox might be too hairy for his readers, even though Martin Gardner explained it in his original Flowsnake piece. So I made an mgif (gosper.org/flake.gif) illustrating the problem, and offering a URL for an (indirect) explanation. --rwg _______________________________________________
-- Mike Stay - metaweta@gmail.comhttp://www.cs.auckland.ac.nz/~mikehttp://reperiendi.wordpress.com
_____________________________________________ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Surely some mistake - the fractal version also works with hexagons ? i.e. with something of unit boundary dimension. Or am I going insane ? On 4 Oct 2013, at 21:29, Dan Asimov wrote:
Guess: It's 1/21 of the large figure.
--Dan
On 2013-10-04, at 1:27 PM, Dan Asimov wrote:
That's a really cool demo!
I wonder what the area is of the triangular figure of the map-of-France at the moment the 3 "segments" first touch.
--Dan
On 2013-10-04, at 11:47 AM, Bill Gosper wrote:
Mike Stay>That's great! May I suggest that when the area is smallest, you should give those three regions the labels 1, 2, and 3?
Thanks! How's http://gosper.org/flaky.gif ?
--rwg
On Fri, Oct 4, 2013 at 2:41 AM, Bill Gosper <billgosper@gmail.com> wrote:
Funster Gary Antonick (NYT NumberPlay) fears that the Franceflake fractal boundary paradox might be too hairy for his readers, even though Martin Gardner explained it in his original Flowsnake piece. So I made an mgif (gosper.org/flake.gif) illustrating the problem, and offering a URL for an (indirect) explanation. --rwg _______________________________________________
-- Mike Stay - metaweta@gmail.comhttp://www.cs.auckland.ac.nz/~mikehttp://reperiendi.wordpress.com
_____________________________________________ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.
The mistake is leaving out the condition that the larger figure be similar to the smaller one. Seven hexagons are not similar to one, but seven Franceflakes are similar to one. On Fri, Oct 4, 2013 at 2:38 PM, David Makin <makinmagic@tiscali.co.uk> wrote:
Surely some mistake - the fractal version also works with hexagons ? i.e. with something of unit boundary dimension. Or am I going insane ?
On 4 Oct 2013, at 21:29, Dan Asimov wrote:
Guess: It's 1/21 of the large figure.
--Dan
On 2013-10-04, at 1:27 PM, Dan Asimov wrote:
That's a really cool demo!
I wonder what the area is of the triangular figure of the map-of-France at the moment the 3 "segments" first touch.
--Dan
On 2013-10-04, at 11:47 AM, Bill Gosper wrote:
Mike Stay>That's great! May I suggest that when the area is smallest, you should give those three regions the labels 1, 2, and 3?
Thanks! How's http://gosper.org/flaky.gif ?
--rwg
On Fri, Oct 4, 2013 at 2:41 AM, Bill Gosper <billgosper@gmail.com> wrote:
Funster Gary Antonick (NYT NumberPlay) fears that the Franceflake fractal boundary paradox might be too hairy for his readers, even though Martin Gardner explained it in his original Flowsnake piece. So I made an mgif (gosper.org/flake.gif) illustrating the problem, and offering a URL for an (indirect) explanation. --rwg _______________________________________________
-- Mike Stay - metaweta@gmail.comhttp://www.cs.auckland.ac.nz/~mikehttp://reperiendi.wordpress.com
_____________________________________________ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Ah - sorry I just looked at the animation page, guess I should have read all the previous mails first ;) On 4 Oct 2013, at 21:54, Mike Stay wrote:
The mistake is leaving out the condition that the larger figure be similar to the smaller one. Seven hexagons are not similar to one, but seven Franceflakes are similar to one.
On Fri, Oct 4, 2013 at 2:38 PM, David Makin <makinmagic@tiscali.co.uk> wrote:
Surely some mistake - the fractal version also works with hexagons ? i.e. with something of unit boundary dimension. Or am I going insane ?
On 4 Oct 2013, at 21:29, Dan Asimov wrote:
Guess: It's 1/21 of the large figure.
--Dan
On 2013-10-04, at 1:27 PM, Dan Asimov wrote:
That's a really cool demo!
I wonder what the area is of the triangular figure of the map-of-France at the moment the 3 "segments" first touch.
--Dan
On 2013-10-04, at 11:47 AM, Bill Gosper wrote:
Mike Stay>That's great! May I suggest that when the area is smallest, you should give those three regions the labels 1, 2, and 3?
Thanks! How's http://gosper.org/flaky.gif ?
--rwg
On Fri, Oct 4, 2013 at 2:41 AM, Bill Gosper <billgosper@gmail.com> wrote:
Funster Gary Antonick (NYT NumberPlay) fears that the Franceflake fractal boundary paradox might be too hairy for his readers, even though Martin Gardner explained it in his original Flowsnake piece. So I made an mgif (gosper.org/flake.gif) illustrating the problem, and offering a URL for an (indirect) explanation. --rwg _______________________________________________
-- Mike Stay - metaweta@gmail.comhttp://www.cs.auckland.ac.nz/~mikehttp://reperiendi.wordpress.com
_____________________________________________ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.
Here's a clickable version of the URL included in Bill's excellent animation http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Fractals.html On Fri, Oct 4, 2013 at 2:26 PM, David Makin <makinmagic@tiscali.co.uk>wrote:
Ah - sorry I just looked at the animation page, guess I should have read all the previous mails first ;)
On 4 Oct 2013, at 21:54, Mike Stay wrote:
The mistake is leaving out the condition that the larger figure be similar to the smaller one. Seven hexagons are not similar to one, but seven Franceflakes are similar to one.
On Fri, Oct 4, 2013 at 2:38 PM, David Makin <makinmagic@tiscali.co.uk> wrote:
Surely some mistake - the fractal version also works with hexagons ? i.e. with something of unit boundary dimension. Or am I going insane ?
On 4 Oct 2013, at 21:29, Dan Asimov wrote:
Guess: It's 1/21 of the large figure.
--Dan
On 2013-10-04, at 1:27 PM, Dan Asimov wrote:
That's a really cool demo!
I wonder what the area is of the triangular figure of the map-of-France at the moment the 3 "segments" first touch.
--Dan
On 2013-10-04, at 11:47 AM, Bill Gosper wrote:
Mike Stay>That's great! May I suggest that when the area is smallest, you should give those three regions the labels 1, 2, and 3?
Thanks! How's http://gosper.org/flaky.gif ?
--rwg
On Fri, Oct 4, 2013 at 2:41 AM, Bill Gosper <billgosper@gmail.com> wrote:
Funster Gary Antonick (NYT NumberPlay) fears that the Franceflake fractal boundary paradox might be too hairy for his readers, even though Martin Gardner explained it in his original Flowsnake piece. So I made an mgif (gosper.org/flake.gif) illustrating the problem, and offering a URL for an (indirect) explanation. --rwg _______________________________________________
-- Mike Stay - metaweta@gmail.comhttp:// www.cs.auckland.ac.nz/~mikehttp://reperiendi.wordpress.com
_____________________________________________ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.
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-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/
Suppose we take one map-of-France (MOF) -- by which I mean just the boundary, of Hausdorff dimension equal to log_7(9), and fill it in with 7 copies each shrunk by a linear factor of sqrt(7). And then for each of those we do the same thing . . . ad infinitum. Is there a reasonable way to assign a Hausdorff dimension to the union of all these stages? Hmm -- I suppose it's still d = log_7(9), but with the Hausdorff d-dimensional content = oo. --Dan
="Mike Stay" <metaweta@gmail.com> The mistake is leaving out the condition that the larger figure be similar to the smaller one. Seven hexagons are not similar to one, but seven Franceflakes are similar to one.
=David Makin <makinmagic@tiscali.co.uk> Surely some mistake - the fractal version also works with hexagons ? i.e. with something of unit boundary dimension. Or am I going insane ?
Sufficient, but not necessary. I suffered similar confusion (but then...) In order to be Certifiable for Classroom Use, along with the link, the text might say something like "tripling the boundary *while preserving the shape* of a 2-dimensional figure". And label the diagrams "Triangle", "Square" and "Franceflake" (except you can't seem to goog on the later, tsk tsk).
participants (6)
-
Bill Gosper -
Dan Asimov -
David Makin -
Marc LeBrun -
Mike Stay -
Thane Plambeck