Shape as Memory Storage - Ambient Intelligence for Scientific Discovery - page 98

It is also worth having a simple phrase to summarize the effect of the transition,
as follows: Notice that the main effect in Fig 17 is that the initial resistance
process is pushed to either side by the breaking-through of an downward inden-
tation. Thus the transition can be summarized by the following phrase:

Breaking-through of an indentation.

17 The Process-Grammar

Having completed the bifurcations, let us now put together the entire system
that has been developed in sections 8 to 17. Our concern has been to describe
the shape evolution by what happens at the most significant points on the shape:
the curvature extrema. We have seen that the evolution of any smooth shape
can be decomposed into into six types of phase-transition defined at the extrema
involved. These phase-transitions are given as follows:

Process Grammar

Cm

+ :

m

+

−→ m − 0

0 (squashing continues till it indents)

CM − : M −

−→ 0 M

+ 0

(resistance continues till it protrudes)

BM

+ :

M

+

−→ M

+

m

+

M

+ (sheild-formation)

Bm − : m − −→ m − M − m − (bay-formation)

+ : + + + + (breaking-through of a protrusion)

Bm m −→ m M m

BM − : M − −→ M − m − M − (breaking-through of an indentation)

Note that the first two transitions are the two continuations, as indicated by
the letter

at the beginning of the first two lines; and the last four transitions are
the bifurcations, as indicated by the letter

C

B at the beginning of the remaining

lines.

18 Scientific Applications of the Process-Grammar

As soon as I published the Process-Grammar in 1988, scientists began to apply
it in several disciplines; e.g., radiology, meteorology, computer vision, chemical
engineering, geology, computer-aided design, anatomy, botany, forensic science,
software engineering, urban planning, linguistics, mechanical engineering, com-
puter graphics, art, semiotics, archaeology, anthropology, etc.
It is worth considering a number of applications here, to illustrate various
concepts of the theory. In meteorology, Milios [9] used the Process-Grammar to
analyze and monitor high-altitude satellite imagery in order to detect weather
patterns. This allowed the identification of the forces involved; i.e., the forces
go along the arrows. It then becomes possible to make substantial predictions
concerning the future evolution of storms. This work was done in relation to the
Canadian Weather Service.
It is worth also considering applications by Shemlon [11], in biology. Shem-
lon developed a continuous model of the grammar using an elastic string equa-
tion. For example, Fig 18 shows the backward time-evolution, provided by the