DYNAMICS OF FUDLS

                Belief creates the actual fact.

William James

Date and time

Dynamics of fudls is limited to their oscillations and interactions.
Fudls every chronon with probability of P = 1/2 spontaneously change the direction to the opposite.
They also interact with each other: the oscillated fudl with probability of P = 1/2 stimulates oscillations adjacent to it fudls, but not oscillated fudl with probability of P = 1/2 suppresses oscillations adjacent to it fudls.
Contact interactions should be considered pairwise. In each top of the Lattice meet up to 6 edges-fudls and, every fudl occurs to 15 pair interactions.
As except fudls there are no other objects, there are no mediators of their contact interactions, and in the mediated interactions mediators are fudls.
All interactions happen at the same time and instantly, extend with infinitely high speed – practically and theoretically.

If the reader had a question "From where fudls take energy for oscillations?", so it should begin reading my articles since the beginning!

Dynamics of fudls is non-linear, so, in the Lattice the self-organization phenomenon takes place: formation of autowaves and autosolitons.

THE ELEMENTARY EXAMPLES

DYNAMICS OF CONDITIONALLY ISOLATED FUDL

The matrix of potential oscillations of the isolated fudl consists of one element which irrespective of the previous oscillations of a fudl, completely in a random way in turn accepts one or the other possible values: 1 or 0.
Analogy: the probability of loss of "tails" when throwing at random of a coin is always equal in accuracy 1/2.
We neglect matrices of potential and actual interactions as we believe that the fudl is isolated.
The matrix of an actual oscillation of the isolated fudl is always equal to its matrix of a potential oscillation as there are no interactions with other fudls.
The matrix of the instantaneous condition of a fudl consists of one element (1 or −1) which, depending on the next value of a matrix of an actual oscillation (1 or 0), respectively changes or does not change the value.
The fudl does not make turns. It does not happen in the transient states. Simply it instantly changes the direction to the opposite.
Our Hypothetical Observer to whom the fudl is represented an arrow, will see that the tip suddenly appeared on other end of an arrow.

DYNAMICS OF CONDITIONALLY ISOLATED PAIR OF FUDLS

The matrix of potential oscillations P of this system consists of two elements which independently from each other and from the previous oscillations and interactions, completely in a random way in turn accept one or the other possible values: 0 or 1.
The matrix of potential interactions U of pair of fudls consists of four elements, two of which (on the main diagonal) – zero, and two elements which independently from each other, completely in a random way can be 0 or 1.
Matrixes are written down in a short form below: only elements of the secondary diagonal are given.

If U = (0  0), fudls do not influence at each other;

if U = (0  1), the first fudl does not influence the second, and the second influences the first;

if U = (1  0), the first fudl influences the second, and the second does not influence the first;

if U = (1  1), both fudls influence at each other.

The reduced matrix of actual interactions V of pair of fudls consists of two elements (1 or 0) which depend on matrix U elements as follows:

if U = (0  0), V = (0  0);

if U = (0  1), V = (0  1);

if U = (1  0), V = (1  0);

if U = (1  1), V = (0  0).

In the latter case interactions are mutually compensated.

The reduced matrix of actual oscillations R of system consists of two elements (1 or 0) which depend on elements P and V:

if P any and V = (0  0), R = P;

if P = (0  0) and V any, R = (0  0);

if P = (1  1) and V any, R = (1  1);

if P = (0  1) and V = (0  1), R = (1  1);

if P = (0  1) and V = (1  0), R = (0  0);

if P = (1  0) and V = (0  1), R = (0  0);

if P = (1  0) and V = (1  0), R = (1  1).

The matrix of the instantaneous condition M of system consists of two elements (1 or −1) which, depending on the corresponding value R (1 or 0), change or do not change the value:

if M any and R = (0  0), Mnew = M;

if M any and R = (1  1), Mnew = −M;

if M = (−1  −1) and R = (0  1), Mnew = (−1  1);

if M = (−1  −1) and R = (1  0), Mnew = (1  −1);

if M = (1  −1) and R = (0  1), Mnew = (1  1);

if M = (1  −1) and R = (1  0), Mnew = (−1  1);

if M = (1  1) and R = (0  1), Mnew = (1  −1);

if M = (1  1) and R = (1  0), Mnew = (−1  1).

DYNAMICS OF CONDITIONALLY ISOLATED
SYSTEM OF THREE AND MORE FUDLS

In case of a chain of three fudls the quantity of the options similar the aforesaid is equal 128 (8 options of the instantaneous condition of system × 16 options of interactions), and in case of three fudls with the common top – 512 (8 options of the instantaneous condition of system × 64 options of interactions). If three fudls formed a triangle, the number of options would also be equal 512, however in the Lattice there are no triangles. In the drawing given here the interaction graph of three fudls with the common top is represented (or forming a triangle). The interaction graph of three fudls in a line-up turns out from it the complete removal of an edge 1_3.
The graph of interactions represented here is a cycle therefore fudls 1, 2 and 3 oscillate as if interactions are not present.
Attention: in the graph arrows showed interactions, but not fudls! Fudls are conditionally presented by green circles here.
Consideration of all options would take too much place here.

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