Shape as Memory Storage - Ambient Intelligence for Scientific Discovery - page 97

squashing process is pushed to either side by the breaking-through of an upward
protrusion. Thus the transition can be summarized by the following phrase:

Breaking-through of a protrusion.

M −

16 Bifurcation at

Now we establish the final bifurcation. We examine what happens when the
process at a

M − extremum branches forward in time. As an example, consider

M − in the center of the bay, the left shape, in Fig 17. In accord with Table
1 (p87), the process at this extremum is an internal resistance .
The effect of bifurcation is that

the

M − splits into two copies of itself - the two
copies shown at the two sides of the deepened bay in the right shape. One should
imagine the two copies as sliding over the surface till they reached their current
positions.
The other crucial event is the introduction of a new extremum

m − in the
bottom of the right shape. This is in accord with the bifurcation format described
in section 14. Notice that the downward process here conforms to Table 1 on
p87, which says that a m − extremum always corresponds to a resistance.

Thus the transition from the left shape to the right shape is the replacement
of the

M − extremum in the middle of the left shape by the triple M − m − M −

in the right shape. The transition is therefore:

M − −→ M − m − M − .

BM − meaning Bifurcation at M − .Thusthe

This transition will be labelled

transition is given fully as:

BM − : M − −→ M − m − 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 M − m − M − .

Bifurcation at

(a) (b)

Fig. 17. Bifurcation at M − .