TAILIEUCHUNG - Stephen Wolfram - A New Kind Of Science Episode 10

Tham khảo tài liệu 'stephen wolfram - a new kind of science episode 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | IMPLICATIONS FOR EVERYDAY SYSTEMS I NOTES FOR CHAPTER 8 can exhibit an instability which causes disturbances with certain spatial wavelengths to grow compare page 988 . In his 1952 paper Turing used a finite difference approximation to a pair of diffusion equations to show that starting from a random distribution of concentration values dappled regions could develop in which one or the other chemical was dominant. With purely linear equations any instability will always eventually lead to infinite concentrations but Turing noted that this could be avoided by using realistic nonlinear chemical rate equations. In tile couple of years before his death in 1954 Turing appears to have tried to simulate such nonlinear equations on an early digital computer but my cursory efforts to understand his programs written as they are in a 32-character machine code were not successful. Following Turing s work tile fact that simple reactiondiffusion equations can yield spatially inhomogeneous patterns has been rediscovered with varying degrees of independence many times. In the early 197X s Ilya Prigoglne termed the patterns dissipative structures. Arid in die mid-1970s Hermann Haken considered the phenomenon a cornerstone of what he called synergetics. Many detailed mathematical analyses of linear reactiondiffusion equations have been dune since the 1970s numerical solutions to linear and occasionally nonlinear such equations have also often been found and in recent years explicit pictures of patterns rather than just curves of related functions have commonly been generated. In the context of biological pigmentation patterns detailed studies have been done particularly by Hans Meinhardt and James Murray. Scale of patterm. The visual appearance of a pattern on an actual animal depends greatly on the scale of the pattern relative to the whole animal. Pandas and anteaters for example typically have just a few regions of different color while other animals can have hundreds of regions.

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