Shape as Memory Storage - Ambient Intelligence for Scientific Discovery - page 95

Fig. 15. Bifurcation at m − .

There is also another feature. In the center of the top of the right shape, a new
extremum has been introduced, M − . Note that the process at this extremum is

a resistance , as predicted in Table 1 on p87. This process explains the flattening
in the middle of the bay, relative to the sharpening towards either end of the
bay.
With these facts, one can now describe exactly what occurred in the transi-
tion from the left shape to the right shape: The m − extremum at the top of the

m − M − m − in the right shape. The

left shape has been replaced by the triple,

transition is therefore:

m − −→ m − M − m − .
This transition will be labelled Bm − meaning Bifurcation at m − .Thusthe

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

It will also be worth having a simple phrase to summarize the effect of the
transition in Fig 15. The obvious phrase is this:

Bay-formation.

14 The Bifurcation Format

+ and
m − . The next two sections will describe the remaining two bifurcations. However,
before giving these, it is worth observing that the first two bifurcations allow us
to see that bifurcations have the same format as each other, which is shown as
follows:

The previous two sections established the first two bifurcations: those at M

E −→ EeE.