Scale - Spatial Mathematics: Theory and Practice through Mapping - page 118

WISCONSIN

WALWORTH

ALLEGAN

KENOSHA

VAN BUREN

LAKE

BOONE MCHENRY

MICHIGAN

BERRIEN

KANE

CASS

KALB

ILLINOIS

COOK

DUPAGE

ST. JOSEPH

KENDALL

LAPORTE

LAKE PORTER

INDIANA

WILL

ALLE

MARSHALL

GRUNDY

STARKE

Figure 5.6 Representative fraction, 1:1,155,581. Source: US Census Bureau, TIGER
web (beta), http://tigerweb.geo.census.gov/tigerweb/

zooming in. TIGERweb (US Census Bureau) has visibility of layers that is scale
dependent. There is an assigned data range within which a given attribute is
visible. In regard to the coastline of Lake Michigan, a bit more detail has come
into focus but still it is quite smooth.

Zoom in even more ( Figure 5.7 with a representative fraction of 1:288,895).
Again, extra detail enters the picture as the scale becomes more local than
in Figure 5.6. Note the structures jutting out into the lake: Promontories and
piers, bays and inlets—natural and man-made structures (can you tell which
is which?). The man-made structures should be more angular. Remember that
much of Chicago's Lake Michigan shoreline has been altered; even much of
the eastern portion of the downtown is built on land filled and reclaimed from
the lake (Mayer and Wade, 1973)!

If you were measuring the coastline length, and were using string, do
you see that you would need much more string when the view is detailed
than when it is general? Measurements, too, are often scale-dependent
(Mandelbrot, 1983). As the map becomes more detailed, the length of the
coastline increases, because more irregularities of the coast become visible.
Thus, even the coastline of a relatively smooth-shored lake such as Lake
Michigan, at an extremely detailed scale, becomes an almost impossibly
large number to measure.

After trying this exercise using TIGERweb ( Figure 5.7 gives QR code access),
try one of the Esri-based exercises, or another exercise that is linked at the