Shape as Memory Storage - Ambient Intelligence for Scientific Discovery - page 92

Fig. 13. Continuation at M − .

11 Continuation at M −

We will now investigate what happens when the process at the fourth and final
extremum M −

in the center of the bay in the left shape in Fig 13. In accord with Table 1 (p87),
the process at this extremum is an internal resistance . In order to understand
this process, let us suppose that the left shape represents an island. Initially, this
island was circular. Then, there was an inflow of water at the top (creating a dip
inwards). This flow increased inward, but met a ridge of mountains along the
center of the island. The mountain ridge acted as a resistance to the inflow of
water, and thus the bay was formed. In the center of the bay, the point labelled
M − is a curvature extremum, because it is the point on the bay with the least
amount of bend (i.e., extreme in the sense of “least”).
Now return to the main issue of this section: What happens when the up-
ward resistive arrow (terminating at the

M − is continued forward in time. As an example, consider the

M − extremum) is continued along the
direction of the arrow. This could happen for example, if there is a volcano in
the mountains, that erupts, sending lava down into the sea. The result would
therefore be the shape shown on the right in Fig 13. In other words, a protrusion
would be formed into the sea.
The structural change, in going from the left to the right shape, should be
understood as follows: First, the

M − in the center of the bay (left shape) changes

+ at the top of the right shape, the protrusion.
An extra feature should be observed: On either side of the

into the M

+ extremum,
at the top of the right shape, a small circular dot has been placed. Such a dot
again marks a position where the curvature is zero; i.e., the curve is, locally,
completely straight.
Thus we can describe what has happened in the transition from the left
shape to the right shape: The

M

M − extremum in the bay of the left shape has

+ extremum at the top of the right shape, and two points
of zero curvature, 0, have been introduced on either side of the

changed into a M

+ .Inother

M

M − in the left shape has been replaced by the triple, 0

+ 0inthe

words, the M

right shape. The transition is therefore:

M − −→

+ 0

0 M .