422 PRINCIPLES OF EMBRYOLOGY 



spread should be taking place the process is brought to a standstill, and 

 the intermediate stages of the diffusion are revealed. Henke calls patterns 

 formed in this way 'spreading fields'. The edges of such fields may often 

 be outlined by some product of a reaction between the substances charac- 

 teristic of the two areas. 



How far does this account of some fundamental types of pattern forma- 

 tion, which was primarily based on the analysis of lepidopteran wings, 

 provide us with an explanation of the kind of phenomena which we meet 

 in the development of embryonic organs in general? It is obvious that a 

 step of the greatest importance would have been taken if we had reached 

 an adequate understanding of the spontaneous appearance of rhythmic 

 or periodic patterns within an originally uniform area. Henke rather 

 vaguely suggests that this may be due to competition between originally 

 irregular spots. Turing (1952) in a paper with the challenging title of 

 'The Chemical Basis of Morphogenesis', has elaborated a mechanism by 

 which a regular pattern might arise witliin a completely homogeneous 

 system. He considers a region (imagine a plane two-dimensional area to 

 make it simpler) in which a number of chemical reactions are proceeding. 

 If these interact with one another by involving the same substances, or by 

 producing products which act as catalysts or affect the rates of other re- 

 actions in any way, then the straightforward situation would be the 

 attainment of some sort of balanced equihbrium condition throughout 

 the whole area. But such an equihbrium is only a statistical phenomenon; 

 actually the system will be disturbed by shght chance variations from 

 place to place. Now it is easy to imagine special systems of reactions such 

 that the equilibrium is unstable; if by chance one substance appears at a 

 certain place in slightly too high a concentration, it will go on increasing. 

 From each such 'high' spot, the substance will diffuse outwards, so that the 

 spots will gradually enlarge. Turing has set up mathematical equations 

 for such systems, and, choosing some arbitrary figures to express the rates 

 of the reactions and of the diffusions, has solved them by means of a 

 modern computing machine. He found that under certain conditions one 

 might expect to get a pattern of a few fairly large areas or irregular 

 blotches of high values of some particular substance. Moreover in some 

 circumstances, the pattern might be more regular, showing a rhythm 

 Mdth a definite wave-length dependent on the physical and chemical 

 magnitudes controlling the reactions. 



Turing compares his 'chemical wave-length' with the interval between 

 regularly appearing structures in an animal or plant. For instance, if the 

 circumference of the cyhndrical body of a Hydra were just about six times 

 the wave-length, one might attribute the animal's hexagonal symmetry, 



