Cell Language Theory, The: Connecting Mind And Matter

The Universality of the Irreducible Triadic Relation 389

“6x9” b2861 The Cell Language Theory: Connecting Mind and Matter

9.4.3 Belousov–Zhabotinsky (BZ) Reaction (or the Brusselator)

The Brusselator is probably the simplest theoretical model of chemical

reactions that can self-organize. See the video at http://en.wikipedia.org/

wiki/Brusselator (Prigogine pointed out to me in 1984 in Austin that the

key step in the Brusselator is the “termolecular” step, i.e., 2X → 3X). The

BZ reaction has the following four chemical steps involving reactants, (A

+ B); products, (D + E); and the transient intermediates, (X + Y), that

interact obeying the following rules or mechanisms:

I suggest that the Brusselator (Figure 9.8) can be mapped onto the

ur-category (Figure 9.2), as shown in Figure 9.9. Mathematically

speaking, Figures 9.2 and 9.9 are isomorphic (i.e., embody similar regu-

larities or principles).

F(n + 1) =F(n) +F(n –1)

Replication(e.g.,squaring)

Variation(e.g., by addition of the old rectangle)

Growth(replication with internal constraints)

Evolution(replication with external constraints)

Figure 9.7 A diagrammatic representation of the “theory” of “RV” (Replication with

Variation) as the fundamental mechanism underlying the generation of the Fibonacci num-

bers, development/growth, and evolution. The Fibonacci numbers and hence RV are found

in DNA [386, 387].

A X

2X + Y 3X

B + X Y + D

X E

______________________________

A + B D + E

Figure 9.8 The Brusselator — a theoretical model of self-organizing chemical reactions,

both organic and inorganic (http://en.wikipedia.org/wiki/Brusselator).

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