[math-fun] why does the amazon river from space look like blood vessels?
Hi all, I'm curious about what seems to be a branching pattern shared by blood vessels, the amazon river and oak trees, among other things. Can anyone point me in the right direction to learn a bit more about this? Here are some examples: - the amazon river<http://www.nasa.gov/centers/goddard/images/content/103371main_amazon-river.gif> - blood vessels<http://www.istockphoto.com/file_thumbview_approve/6303204/2/istockphoto_6303204-blood-vessels.jpg> - lightning<http://www.istockphoto.com/file_thumbview_approve/3506509/2/istockphoto_3506509-lightning.jpg> - an oak tree<http://www.telegraph.co.uk/news/uknews/4697449/Oak-tree-dating-back-250-years-crashes-to-the-ground-in-Devon.html> What I find interesting are the odd details. An oak tree, lightning, and blood vessels, for example, seem to have these odd double-back knotted points. Things that — to me — do not look this this are.. - a winding river<http://www.istockphoto.com/file_thumbview_approve/4280336/2/istockphoto_4280336-meandering-river-cattle-balloon.jpg> - veins in this leaf<http://www.istockphoto.com/file_thumbview_approve/3569643/2/istockphoto_3569643-green-leaf-3.jpg> - a crack in ice<http://www.istockphoto.com/file_thumbview_approve/11913741/2/istockphoto_11913741-ice-texture.jpg> I actually expected a crack in ice to look a lot more like lightning but it's completely different. These also seem to have their own groupings. The grand canyon<http://earthobservatory.nasa.gov/IOTD/view.php?id=6929> looks like frost<http://www.masterfile.com/stock-photography/image/600-02912692/Close-up-of-Frost>, for example. But I'm particularly curious about the blood vessels/amazon pattern. Cheers, Gary
Gary Antonick:
I actually expected a crack in ice to look a lot more like lightning but it's completely different.
How about *these* cracks? http://chesswanks.com/pix/fractals.jpg
How about this Lichtenberg figure? http://lh3.ggpht.com/mgmirkin/Rm8lRYYGgVI/AAAAAAAAA-o/ypKAE8rjiTc/human_LF2.... On Mar 5, 2011, at 7:24 PM, Hans Havermann <pxp@rogers.com> wrote:
Gary Antonick:
I actually expected a crack in ice to look a lot more like lightning but it's completely different.
How about *these* cracks?
http://chesswanks.com/pix/fractals.jpg
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quadricode - Yes. Thanks. Lichtenberg figure<http://en.wikipedia.org/wiki/Lichtenberg_figure>is very interesting. But it doesn't look like lightning. But now I think I get it. Lightning must be a slow crack. The Hans Haverman link is perfect: the ice is is slowly melting rather than shattering. Oak trees grow very slowly. Lightning, even though it seems really fast, must be traveling a lot more slowly than it could in other conditions. And that helps explain, I think, what was confusing to me about blood vessels. The fractal changes. A fat vessel like the aorta looks like the tree in the Hans Haverman ice link: smaller branches jut out at more perpendicular angle to the main branch because that's most efficient. But at the capillaries blood vessels are messy and odd — like an oak. I think that's it. Kind of like how meandering country roads don't look like miniature freeways. The fractal isn't uniform. Real blood vessels don't look this <http://www.flexilearn.com/?p=9> this for example. On Sat, Mar 5, 2011 at 6:08 PM, <quadricode@gmail.com> wrote:
How about this Lichtenberg figure?
http://lh3.ggpht.com/mgmirkin/Rm8lRYYGgVI/AAAAAAAAA-o/ypKAE8rjiTc/human_LF2....
On Mar 5, 2011, at 7:24 PM, Hans Havermann <pxp@rogers.com> wrote:
Gary Antonick:
I actually expected a crack in ice to look a lot more like lightning but it's completely different.
How about *these* cracks?
http://chesswanks.com/pix/fractals.jpg
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Gary Antonick:
The Hans Havermann link is perfect: the ice is is slowly melting rather than shattering.
I took that photo of a shallow pond on 23 November 2008 in Toronto's High Park. The water was freezing rather than melting and there might have been an upwelling of current (I conjecture) at the hubs of of those radiating spokes.
Hans — amazing. that's exactly it. On Sat, Mar 5, 2011 at 5:24 PM, Hans Havermann <pxp@rogers.com> wrote:
Gary Antonick:
I actually expected a crack in ice to look a lot more like lightning but
it's completely different.
How about *these* cracks?
http://chesswanks.com/pix/fractals.jpg
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