A brief overview of cellular automata and its applications

Talk about some of your own learning, please correct me if there are mistakes.

Cellular automata (Cellular automata) was the early 1950s by the father of the computer von Neumann (J.

Von Neumann) is proposed to simulate the self-replicating capabilities of a life system. Since then, Stephen Wolfram has carried out a thorough study of cellular automata theory, for example, he has studied the models produced by all 256 rules of one-dimensional elementary Stephen Wolfram, and divided the cellular automata into stationary, periodic, chaotic and complex 4 types.

The cellular automata uses discrete spatial layouts and discrete time intervals to divide the cell into finite states, the cellular the evolution of an individual state is related only to its current state and the state of one of its local neighborhoods.

Cellular automata is a method of computer modeling and simulation, which is based on a large number of biological cells (cell) and

The macroscopic behavior and law of the complex system composed by the individual of the row unit. L-System, finite condensation diffusion, lattice gas automata [1-2], Lattice Boltzmann method [3], traffic flow model, etc. are the embodiment of cellular automata, they all have important theoretical significance and practical application value. The cellular automata method is a powerful tool for the study of complex systems, and is an important growing point of new methods and disciplines [4].

Basic elements of Elementary cellular automata (elementary Cellular automata, ECA) are as follows

• Space : a single-dimensional straight line of the point of fine spacing. Can be a set of integer points on a range.
• The state set : S={s1,s2} is only two different states. These two different states can be encoded as 0 and 1, respectively, if the graphic representation, you can correspond to "black" and "white" or the other two different colors.

• Neighbor : Take the neighbor radius r=1, that is, each cell has a maximum of "neighbors" two neighbors.
• Evolution rules : Arbitrarily set, up to 2^8=256 different set-up mode. The cells are neighbors with 8 cells adjacent to each other. That is, Moore's neighbor; The life and death of a cell by its own state of life and death in the moment itself and the state of the surrounding eight neighbors.

Like what:

ECA #76 = (01001100) 2

ECA #184 = (10111000) 2
The embryonic form of traffic flow "single lane heel" (no overtaking allowed)

ECA #90 = (01011010) 2

"Neighbors" Module 2 addition

Similar to Sierpinski triangles

Finally , the application of cellular automata is discussed.

The cellular automata method is a framework model, which does not have to be rigid, but rather a simulation ideology that is considered from the standpoint of pragmatism. The main point of cellular automata simulation is to capture the basic characteristics of the phenomena studied.

In the actual application process, some of the characteristics of some of the cellular automata models have been extended, some in the rule design to introduce random factors, such as: Forest fire model. Another example, in the traffic, communications developed today, the study of epidemics or computer virus transmission problem, we can also change the spatial background to complex network nodes, with the network adjacency point as a neighbor. Such adjustments are clearly more realistic than the models that still use the two-dimensional Euclidean space and Euclidean distance. In the simulation study of population emergency evacuation in large-scale places, we can consider the factors of age and sex, that is, the cell is not homogeneous, and it is more advantageous to make the simulation system close to the real system.

Cellular automata will be simple and complex, microscopic and macroscopic, local and global, finite and infinite, discrete and continuous, etc.
A pair of philosophical categories is closely linked together, it is expected to be a tool to explore complex science.

S. Wolfram has said:

You

should learn the cellular automata before learning linear algebra.

Reference documents:

[1] Hardy J, Pomeau Y, de Pazzis O. Time evolution of a two-dimensional model system. J.math. Phys., 14:1746-1759, 1973

[2] frish U, Hasslacher B, Pomeau Y. Lattice-gas automata for the Navier-stokes Equation.phys. Rev. Lett., 56:1505-1508, 1986

[3] Qian Y (Yu grandsolar), d ' Humiéres D, Lallemand P. Lattice BGK model for Navier-stokes

Equation. Europhys. Lett., 17:479-484, 1992

[4] Wolfram S. A New Kind of Science[m]. Wolfram Media Inc, 2002

A brief overview of cellular automata and its applications