Science, computers, and people: from the tree of mathematics
Science, computers, and people: from the tree of mathematics
On the Length of Programs for Computing Finite Binary Sequences: statistical considerations
Journal of the ACM (JACM)
The program-size complexity of self-assembled squares (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Running time and program size for self-assembled squares
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
A new kind of science
Information and Randomness: An Algorithmic Perspective
Information and Randomness: An Algorithmic Perspective
Algorithmic self-assembly of dna
Algorithmic self-assembly of dna
Complexities for generalized models of self-assembly
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Computation: finite and infinite machines
Computation: finite and infinite machines
Theory of Self-Reproducing Automata
Theory of Self-Reproducing Automata
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Visualization 2001 Conference (Acm
Visualization 2001 Conference (Acm
Small weakly universal turing machines
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
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Despite having advanced a reaction---diffusion model of ordinary differential equations in his 1952 paper on morphogenesis, reflecting his interest in mathematical biology, Turing has never been considered to have approached a definition of cellular automata. However, his treatment of morphogenesis, and in particular a difficulty he identified relating to the uneven distribution of certain forms as a result of symmetry breaking, are key to connecting his theory of universal computation with his theory of biological pattern formation. Making such a connection would not overcome the particular difficulty that Turing was concerned about, which has in any case been resolved in biology. But instead the approach developed here captures Turing's initial concern and provides a low-level solution to a more general question by way of the concept of algorithmic probability, thus bridging two of his most important contributions to science: Turing pattern formation and universal computation. I will provide experimental results of one-dimensional patterns using this approach, with no loss of generality to a n-dimensional pattern generalisation.