
72 Polytope Projects
Observe that the commutation condition: DU–UD=I is verifi ed and the
two rooted trees are 1-dual.
3.3.2 Self-Evolvability and Polytopes
Structures obtained as superposition of the dual graded schemas are
considered as potentially self-evolvable.
Figure 3.26 shows the potentially self-evolvable rooted trees.
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Fig. 3.26 Self-evolvable rooted trees.
It shows “up” transitions, U, in the schemas denoted by thick trees and
thick arrows and “down” transitions, D, in the schemas, denoted by thin
trees and thin arrows.
We need to consider the coupling of both directions U and D.
The operator U describes the confi guration process starting ...