What is the Turing equation?

What is the Turing equation?

Two-component reaction–diffusion equations An important idea that was first proposed by Alan Turing is that a state that is stable in the local system can become unstable in the presence of diffusion. with f (u) = λu − u3 − κ which describes how an action potential travels through a nerve.

What is a Turing type mechanism?

Turing proposed a model wherein two homogeneously distributed substances (P and S) interact to produce stable patterns during morphogenesis. These patterns represent regional differences in the concentrations of the two substances. Their interactions would produce an ordered structure out of random chaos.

Can Turing machines compute anything?

The Turing machine can compute anything that can be computed. It is the very definition of computation and the fundamental tool for reasoning about computers.

What is embryo patterning?

During embryonic patterning, genetic programs are precisely coordinated to create complex tissues and organs. Genome sequencing and forward genetic screens have revealed an extensive list of patterning genes, many of which are expressed in a tissue-specific manner at discrete time points in embryo development.

Why is Turing machine more powerful than FSM?

But only a Turning machine can recognise a sequence that has an arbitrary number of As followed by the same number of Bs. That is a Turing machine is more powerful than a finite state machine because it can count.

Is Turing machine powerful than PDA?

Turing machines are indeed more powerful than regular PDAs. However in special case of a PDA with two stacks (TPDA or 2-PDA) the TPDA is equally powerful than a turing automata. And thus the TPDA can simulate the work of a Turing machine, and they are equivalent.

What is the formula for a Turing machine?

Purely formally a Turing machine can be specified as a quadruple T = (Q, Σ, s, δ) where: 1 Q is a finite set of states q 2 Σ is a finite set of symbols 3 s is the initial state s ∈ Q 4 δ is a transition function determining the next move: δ: (Q × Σ) → (Σ × {L, R} × Q)

What is a Turing pattern in chemistry?

Turing pattern. The English mathematician Alan Turing introduced a concept, which came to be known as a Turing pattern, in a 1952 paper entitled ” The Chemical Basis of Morphogenesis “. This foundational paper describes how patterns in nature, such as stripes and spots, can arise naturally and autonomously from a homogeneous, uniform state.

Is the Turing model of reaction–diffusion a model for pattern formation?

Reaction–diffusion systems have attracted much interest as a prototype model for pattern formation. Patterns such as fronts, hexagons, spirals, stripes and dissipative solitons are found as solutions of Turing-like reaction–diffusion equations.

What does it mean for a function to be Turing computable?

The second concerns the definition of Turing computable, namely that a function will be Turing computable if there exists a set of instructions that will result in a Turing machine computing the function regardless of the amount of time it takes.