By Hermann Haken
This e-book offers the recommendations had to take care of self-organizing complicated structures from a unifying viewpoint that makes use of macroscopic facts. some of the meanings of the concept that "information" are mentioned and a normal formula of the utmost info (entropy) precept is used. through effects from synergetics, sufficient goal constraints for a wide type of self-organizing structures are formulated and examples are given from physics, biology, and laptop technology (pattern popularity via parallel computers). The extensions inside the moment version express how, in keeping with very likely scarce and noisy facts, impartial guesses approximately tactics of complicated platforms could be made and the underlying deterministic and random forces made up our minds. This process permits probabilistic predictions of approaches, with functions to varied fields starting from know-how via biology and drugs to economic climate. the connection to chaos conception is usually addressed.
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Extra resources for Information and self-organization: a macroscopic approach to complex systems
Several pseudo-random number generators (PRNG) have been proposed which are using the form of elliptic curves. Since  methods, diﬀerent approaches for extracting pseudo-randomness from elliptic curves have been proposed such as [9–12]. The key sequence generators used in this paper is based on the Chaos-Driven Elliptic Curve Pseudo-random Number Generator (C-D ECPRNG) which uses the Linear Congruential Generator on EC (EC-LCG) presented in  with modulation by chaotic maps. The C-D ECPRNG constructions increases randomness of the sequence generated and makes its period (theoretically) inﬁnite since it combines positive properties of both ECPRNG and Chaotic Pseudo-random Number Generators (CPRNG) as discussed in .
Firstly, Koblitz’s method is used for encoding image pixels to EC-points or the mapping method for mapping image pixels to EC-points as well. Secondly, addition of the resulted EC-points from ﬁrst step with the ECpoints resulted from the C-D ECPRNG are done to obtain EC-points encrypted sequences. The decryption process is done vice-versa. The two methods implementation was done and the encrypted EC-points was obtained. The obtained EC-points from each step in the proposed image encryption scheme are plotted demonstrated that the encrypted EC-points are uniformly distributed on the used elliptic curves.
To encrypt the EC mapped points resulted from Table 3, we utilize EC-points sequence generated from C-D ECPRNG. In this case, we choose the same generator point G = (502, 23) and initial value U0 = (4, 386) belong to E deﬁned in (11) and the random bits bi generated from the Logistic map deﬁned in Sect. 6701. Table 4 showed how the encryption process works and the EC encrypted points obtained. Rows (1,2) represent pixel indexes and the corresponding pixel values respectively. Rows (3,4) represent EC mapped points resulted from Table 3 and EC-points resulted from C-D ECPRNG respectively.