Shape as Memory Storage - Ambient Intelligence for Scientific Discovery - page 93

CM − meaning Continuation at M − .Thusthe

This transition will be labelled

transition is given fully as:

CM − : M − −→

+ 0

0 M .

This mathematical expression is easy to translate into English. Reading the
symbols, from left to right, the expression says:

M − takes M − and replaces it by the triple 0

+ 0 .

Continuation at M

It is worth having a simple phrase defining the transition in Fig 13. Notice that,
since the extremum M − in the left shape is a resistance, and the extremum

+

M

in the right shape is a protrusion, the transition can be described as:

A resistance continues till it protrudes.

Comment: We have now gone through each of the four extrema, and defined
what happens when the process at the extremum is allowed to continue. The
first and second extrema involved no structural change, but the third and fourth
extrema did.

M +

12 Bifurcation at

We now turn from continuations to bifurcations (branchings) at extrema. Again,
each of the four extrema will be investigated in turn.
First we examine what happens when the process at a

+

M extremum

+ at the top of the left
shape in Fig 14. In accord with Table 1 (p87), the process at this extremum is
a protrusion . The effect of bifurcating is shown in the right shape. One branch
goes to the left, and the other goes to the right.
The structural change, in going from the left to the right shape, should be
understood as follows: First observe that the single

branches forward in time. As an example, consider the M

+ at the top of the left

M

Fig. 14. Bifurcation at M + .