Continuous automaton
Encyclopedia
A continuous automaton can be described as a cellular automaton
extended so the valid states a cell can take are not just discrete (for example, the states consist of integers between 0 and 3), but continuous, for example, the real number range [0,1]. The cells however remain discretely separated from each other. One example is called computational verb cellular network (CVCN)
. , of which the states of cells are in the region of [0,1].
Such automata can be used to model certain physical reactions more closely, such as diffusion
. One such diffusion model could conceivably consist of a transition function based on the average values of the neighbourhood
of the cell. Many implementations of Finite Element Analysis can be thought of as continuous automata, though this degree of abstraction away from the physics of the problem is probably inappropriate.
Continuous spatial automata
resemble continuous automata in having continuous values, but they also have a continuous set of locations rather than restricting the values to a discrete grid of cells.
Cellular automaton
A cellular automaton is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling. It consists of a regular grid of cells, each in one of a finite number of states, such as "On" and "Off"...
extended so the valid states a cell can take are not just discrete (for example, the states consist of integers between 0 and 3), but continuous, for example, the real number range [0,1]. The cells however remain discretely separated from each other. One example is called computational verb cellular network (CVCN)
. , of which the states of cells are in the region of [0,1].
Such automata can be used to model certain physical reactions more closely, such as diffusion
Diffusion
Molecular diffusion, often called simply diffusion, is the thermal motion of all particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size of the particles...
. One such diffusion model could conceivably consist of a transition function based on the average values of the neighbourhood
Neighbourhood
A neighbourhood or neighborhood is a geographically localised community within a larger city, town or suburb. Neighbourhoods are often social communities with considerable face-to-face interaction among members. "Researchers have not agreed on an exact definition...
of the cell. Many implementations of Finite Element Analysis can be thought of as continuous automata, though this degree of abstraction away from the physics of the problem is probably inappropriate.
Continuous spatial automata
Continuous spatial automaton
Continuous spatial automata, unlike cellular automata, have a continuum of locations. The state of a location is a finite number of real numbers. Time is also continuous, and the state evolves according to differential equations...
resemble continuous automata in having continuous values, but they also have a continuous set of locations rather than restricting the values to a discrete grid of cells.