Complexity of the Geological Framework and Use of Mathematics - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 27

Fig. 1.15 (a) Black picture points removed from original pattern after first erosion; (b) and those
added to it after first dilatation (Source: Agterberg and Fabbri 1978 , Fig. 2)

(1) sedimentary rocks, (2) metabasalt, and (3) rhyolitic rock. Only the rhyolitic rock
is shown in Fig. 1.14d . It comprises rhyolite tuff, augen schist, rhyolite crystal tuff
and quartz-sericite schist, rhyolite, minor phyllite and granophyre. Skinner ( 1974 ,
p. 15) said: “A conspicuous feature of the map of the Tetagouche Group in the
Bathurst-Newcastle area is the C-shaped area of rhyolitic rock surrounded by
metabasalt and sedimentary rock. The rhyolitic core has been referred to by some
geologists as a basin structure, and by others, as a dome. The writer believes the
C-shape is the result of two periods of folding. Apparently the Tetagouche Group was
folded into northwesterly trending recumbent folds overturned toward the southwest
during the late Ordovician Taconic Orogeny, then refolded about northeasterly
trending axis during the Devonian Acadian Orogeny. If this is so, the rhyolitic core
(map-unit 3) is the youngest part of the group and the surrounding sedimentary rock
(map-unit 1) is the oldest.” The acidic volcanics underlie an area of about 1,259 km 2
but probably covered an area several times larger when originally deposited. Skinner
( 1974 , p. 28) suggested an ignimbritic (pyroclastic flow) origin for most of these rocks.
Every picture point or pixel on a square grid or raster can be accessed indivi-
dually. The eight pixels around any black pixel belonging to the binary image of
Fig. 1.14d are either white or black. Suppose that they are changed into black pixels
if they are white. This operation is termed dilatation by eight neighbor square logic.
The result is a new pattern with 23,976 pixels (see Fig. 1.14e ). The difference
between Fig. 1.14d and e consists of 23,976-18,843

5,133 pixels shown separately
in Fig. 1.15b . A second dilatation gives the pattern of Fig. 1.14f . The reverse process
which consists of replacing black pixels that surround white pixels by white ones is
called “erosion”. Three successive erosions of the original pattern (Fig. 1.14d ) result
in Fig. 1.14c , 1.14b and 1.14a , respectively. The black pixels lost during the first
erosion (from Fig. 1.14d to 1.14c ) are shown separately in Fig. 1.15a .
In order to continue discussion of these operations it is convenient to further adopt
terminology as developed by Serra ( 1976 )andWatson( 1975 ). Suppose that the original

¼