Subject: Re: OKTX --finally! figures
Date: Apr 18, 2003 @ 13:33
Author: acroorca2002 ("acroorca2002" <orc@...>)
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> If a fractal is symmetrical over the x-axis, and youthis is the only part i dont get yet
> take the top half as one half the bank of a lake, and
> the bottom half as the other, the line dividing them
> in 2 is finite and completely straight. This seems to
> be the case in The Mandelbrot Set (see Mike's link:
> http://www.mindgames.com/mb.phtml): the midline would
> be a finite horizontal straight line dividing the
> fractal picture exactly in two. Thus we can see that
> in the case of a river, just because the banks might
> be of infinite length (and of a fractal pattern), it
> does NOT mean the midline of the river must be.
> Ok, now given that the banks of a river are not
> completely symmetrical, but there is a convergence
> here to a finite and measurable line since the
> middleline can only exist at one point per each point
> you move down the river, thus not abling it to have
> fractal properties.
> Of course this is only for rivers where the border is__________________________________________________
> in the river. Any river with one of the banks as the
> border (ie old Red River) would naturally follow a
> fractal pattern and have infinite length.
> --- "Brian J. Butler" <bjbutler@b...>
> wrote:
> > On Thursday 17 April 2003 07:58 pm, you wrote:
> > OK, I give up. And I give you an F in fractal
> > geometry.
> > BJB
> >
> > > I really have not misunderstood any of the points
> > made in opposition to
> > > measuring a physical boundary... I have only said
> > that it can be done, and
> > > it is done. I don't agree with the notion that
> > there is infinite length in
> > > a river that flkoiws only, say, 10 miles. That's
> > an absurd notion. A
> > > highway might be measured by its length along a
> > centerline in the median,
> > > while the distance along its outside shoulders may
> > be different... still,
> > > the distance is not infinite! We can prove that by
> > arriving at our
> > > destination.
> > >
> > > Once a high water mark is established, if that is
> > the boundary, then it can
> > > be measured. I didn't say it was easy to go 1,000
> > miles along the banks of
> > > the Red River (I believe the OK-TX boundary is the
> > center of the channel,
> > > which would be much less difficult to measure),
> > but it can be done.
> > >
> > > At a human scale, the water line does not have to
> > be measured around
> > > molecules, or grains of sand, to be called
> > accurate. As with my highway
> > > example.
> > >
> > > -----Original Message-----
> > > From: Brian J. Butler
> > [mailto:bjbutler@b...]
> > > Sent: Thursday, April 17, 2003 4:18 PM
> > > To: BoundaryPoint@yahoogroups.com
> > > Subject: Re: [BoundaryPoint] OKTX --finally!
> > figures
> > >
> > >
> > > On Thursday 17 April 2003 05:04 pm, you wrote:
> > > Let me trry one more time, and then if you still
> > don't get it, I will give
> > > up. Suppose a boundary is defined as the high
> > water mark along a river
> > > bank.
> > > Further suppose the river bank is irregular, which
> > should not be much of a
> > > stretch if you have ever looked at a river bank.
> > The irregularities exist
> > > at
> > > many scales, from broad bends measured in miles,
> > to smaller meanders
> > > measured
> > > in hundreds of feet, to smaller gouges measured in
> > tens of feet, to rocks
> > > meausured in feet, to pebbles measured in inches,
> > to small pebbles, ...
> > > etc.
> > >
> > > Clearly if you consider smaller and smaller
> > irregularities, the length of
> > > the
> > > river bank increases without bound, as illustrated
> > by the two measurements
> > > given for the OK-TX boundary. Since you think the
> > length is bounded, it
> > > implies that you stop measuring around features
> > below some size threshold.
> > > My
> > > question to you is: At what scale do you stop
> > measuring, and why? Please
> > > actually think about the question.
> > > BJB
> > >
> > > > It would really not go on like that. If the
> > boundary is defined, one
> > > > follows that definition. If OK-TX has been
> > defined as a certain location
> > >
> > > in
> > >
> > > > the channel of the Red River, one would follow
> > that and measure it as
> > > > s/he goes. If the menaderings are part of the
> > definition, that would be
> > > > followed.
> > > >
> > > > The hard number really is out there. It is not
> > infinite.
> > > >
> > > > -----Original Message-----
> > > > From: Brian J. Butler
> > [mailto:bjbutler@b...]
> > > > Sent: Thursday, April 17, 2003 1:55 PM
> > > > To: BoundaryPoint@yahoogroups.com
> > > > Subject: Re: [BoundaryPoint] OKTX --finally!
> > figures
> > > >
> > > >
> > > > On Thursday 17 April 2003 12:13 pm, you wrote:
> > > > And following really small meanders
> > > >
> > > > Red River - -1234 miles
> > > > East Panhandle line -- 133.6 miles
> > > > North Panhandle line -- 167 miles (minus 2.2
> > miles TXNM)
> > > >
> > > > Total -- 1532.4 miles
> > > >
> > > >
> > > > And following really small meanders and medium
> > sizes irregularities:
> > > >
> > > > Red River -- 2816 miles
> > > > East Panhandle line -- 133.6 miles
> > > > North Panhandle line -- 167 miles (minus 2.2
> > miles TXNM)
> > > >
> > > > Total -- 3114.4 miles
> > > >
> > > > Etc.
> > > >
> > > > > Including only larger river bends:
> > > > >
> > > > > Red River -- 480.0 miles
> > > > > East Panhandle line -- 133.6 miles
> > > > > North Panhandle line -- 167 miles (minus 2.2
> > miles TXNM)
> > > > >
> > > > > Total -- 778.4 miles
> > > > >
> > > > > Following the smaller meanderings of the
> > rivers:
> > > > >
> > > > > Red River -- 726 miles
> > > > > East Panhandle line -- 133.6 miles
> > > > > North Panhandle line -- 167 miles (minus 2.2
> > miles TXNM)
> > > > >
> > > > > Total -- 1024.4 miles
> > > > >
> > > > > Source: Texas Almanac
> > > > >
> > > > > --Joe
> > > > >
> > > > > (Will post some pics of my visit to Copperhill
> > TN/McCaysville GA soon.
> > > > > The border runs through a grocery store and a
> > church)
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > > Your use of Yahoo! Groups is subject to
> > >
> > > http://docs.yahoo.com/info/terms/
> >
> > --
> > Brian J. Butler
> > BJB Software, Inc.
> > 508-429-1441
> > bjbutler@b...
> > http://www.bjbsoftware.com
> >
>
>
>
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