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The following table indicates the actions to be performed by the Turing machine depending on whether its current state is A or B, and the symbol currently being read is 0, 1 or 2. The table entries indicate the symbol to be printed, the direction in which the tape head is to move, and the subsequent state of the machine.
A state register that stores the state of the Turing machine, one of finitely many. Among these is the special start state with which the state register is initialised. These states, writes Turing, replace the "state of mind" a person performing computations would ordinarily be in.
The theory, which can be called a reaction–diffusion theory of morphogenesis, has become a basic model in theoretical biology. [2] Such patterns have come to be known as Turing patterns. For example, it has been postulated that the protein VEGFC can form Turing patterns to govern the formation of lymphatic vessels in the zebrafish embryo. [3]
Small weakly universal Turing machines that simulate the Rule 110 cellular automaton have been given for the (6, 2), (3, 3), and (2, 4) state-symbol pairs. [17] The proof of universality for Wolfram's 2-state 3-symbol Turing machine further extends the notion of weak universality by allowing certain non-periodic initial configurations.
A 2-state 2-color turmite on a square grid. Starting from an empty grid, after 8342 steps the turmite (a red pixel) has exhibited both chaotic and regular movement phases. In computer science, a turmite is a Turing machine which has an orientation in addition to a current state and a "tape" that consists of an infinite two-dimensional grid of ...
The Turing pattern is a concept introduced by English mathematician Alan Turing in a 1952 paper titled "The Chemical Basis of Morphogenesis" which describes how patterns in nature, such as stripes and spots, can arise naturally and autonomously from a homogeneous, uniform state. [1] [2] The pattern arises due to Turing instability which in turn ...
A further extension of Langton's ants is to consider multiple states of the Turing machine – as if the ant itself has a color that can change. These ants are called turmites, a contraction of "Turing machine termites". Common behaviours include the production of highways, chaotic growth and spiral growth. [7] Some example turmites:
The state of a location is a finite number of real numbers. Certain cellular automata can yield diffusion in liquid patterns in this way. Continuous spatial 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.