Shape as Memory Storage - Ambient Intelligence for Scientific Discovery - page 90

+ . Recall from Table 1 (p87), that the + extremum cor-

First consider M M

+ , the three protru-
sions. We want to understand what happens when any one of the

responds to a protrusion. Fig 11 shows three examples of M

+ processes
is continued. For example, what happens when the protruding process at the top
M

M

+ continues pushing the boundary further along the direction of its arrow?

M + and Fig. 11. Continuation at m − do not change extremum-type.

+ extremum, despite
being extended further upwards. Intuitively, this is obvious: A protrusion remains
a protrusion if it continues. Therefore, from now on, we will ignore continuation
at

The answer is simple: The boundary would remain a M

+ as structurally trivial.
Now observe that exactly the same considerations apply with respect to any
m − extremum. For example, notice that the same shape, Fig 11, has three

M

m −
extrema. Notice also that, in accord with Table 1 (p87), each of these corresponds
to an indentation . It is clear that, if the process continues at a m − , the boundary

m − . Again, this is intuitively obvious: An indentation remains an
indentation if it continues. As a consequence, we will also ignore continuation at
m − as structurally trivial.
In summary, the two cases considered in this section, continuation at

would remain

+

M

m − , are structurally trivial. It will now be seen that continuations at the
remaining two extrema,

and at

+ and

M − , induce much more interesting effects on a m

shape.

m +

10 Continuation at

+ extremum is always associated with a squash-
ing process. An example is shown in the top of the left shape in Fig 12. Notice
therefore that the process explains the flattening at this extremum, relative to
the greater bend at either end of the top.
Our goal is to understand what happens when the process at this

AccordingtoTable1(p87),a m

+ ex-
tremum is continued forward in time; i.e., the downward arrow pushes further
downward. Clearly, a continuation of the process can result in the indentation
shown at the top of the right shape in Fig 12.

m