Pseudorandom Number Generators Based on Cellular Automata With the Hexagonal Coverage

Pseudorandom Number Generators Based on Cellular Automata With the Hexagonal Coverage

DOI: 10.4018/978-1-5225-2773-2.ch007
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Abstract

The seventh chapter describes approaches to constructing pseudo-random number generators based on cellular automata with a hexagonal coating. Several variants of cellular automata with hexagonal coating are considered. Asynchronous cellular automata with hexagonal coating are used. To simulate such cellular automata with software, a hexagonal coating was formed using an orthogonal coating. At the same time, all odd lines shifted to the cell floor to the right or to the left. The neighborhood of each cell contains six neighboring cells that have one common side with one cell of neighborhood. The chapter considers the behavior of cellular automata for different sizes and different initial settings. The behavior of cellular automata with various local functions is described, as well as the behavior of the cellular automaton with an additional bit inverting the state of the cell in each time step of functioning.
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The Principles Of Organization Of The Pseudorandom Number Generator Based On The Cellular Automata With A Hexagonal Coverage

Earlier we looked at the different types of coatings of the CA area and various geometric shapes of the cells. The most popular of the cell geometric shapes are the triangular, rectangular and hexagonal shapes. They give complete coverage of the CA area. Accordingly, various lattices are used, in sites of which are located the CA cells. In addition, cellular automata with different geometric shapes of the cells organizes the various forms of neighborhoods.

At the moment, little attention are paying the specialists the combination of cells with a variety of geometric shapes in one cellular automata. Especially no sense to use different geometric forms of the cells for the implementation of elementary cellular automata. The combination of cells with a variety of geometric shapes is used for the realization of a two-dimensional cellular automata. At the same time the cells forms are adjusted so that the geometric coverage was complete with the maximum density.

A number of advantages have hexagonal shape of the cells (Belan & Motornyuk, 2013; Nicoladie, 2014; Bilan, Motornyuk, & Bilan, 2014; Konstantinos, 2011; Avolio, Ambrosio, Gregorio, Rongo, & Spataro, 2001; Avolio, Di Gregorio, Mantovani, Pasuto, Rongo, Silvano, & Spataro, 1999; Basurto, Leon, Martinez, & Seck-Tuoh-Mora, 2013). The hexagonal coating reduces the influence of the ladder effect, and also gives good results in solving many problems.

A neighborhood of the cells that have a common side with the adjacent cell, is the set of main the cells (Figure 1).

Figure 1.

The cells of the main neighborhood with a hexagonal covering

The hexagonal coating provides unambiguous coating. Each cell has only six nearest neighbors. For the simulation of the hexagonal coating on area, divided into rectangular cells, it necessary to shift all the even lines right to the half of the cage (Figure 2).

Figure 2.

The modeling of the hexagonal covering with a rectangular segmentation of cellular automata area

Cellular automata with a hexagonal covering (HCCA) has a different evolution compared to cellular automata with a rectangular covering (Figure 3).

Figure 3.

The CA evolution with different forms of a coverage

The edge cells are not change own states at every time step of an evolution for CA with hexagonal and triangular coverings. However, their condition has been influenced to the state of the neighboring cells. All the neighborhood for each of the coating are consisted of the nearest cells which have a common side with the control cell.

For hexagonal covering cellular automata, the initial settings are different from the initial settings of the CA with the orthogonal covering. The synchronous and asynchronous CA can be realized by the hexagonal covering cellular automata.

Modeling of the PRNG based on synchronous hexagonal covering cellular automata with a fixed output cell was taken into account such the initial settings.

  • 1.

    The dimension of CA.

  • 2.

    The coordinates of the active cell.

  • 3.

    The local conditions cells function.

  • 4.

    The initial distribution of the cell states.

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