FACTORS IN EMBRYOGENESIS 35 



will subsequently appear), apart from some slight deviations due to 

 Brownian movement and to chance fluctuations in the number of the 

 X and Y molecules that have reacted in the various possible ways in 

 various regions. 



(ii) The concentrations of X and Y will vary slowly as the system 

 adjusts itself to the changing evocator concentration. This change will 

 also result in the fluctuations of concentration smoothing themselves 

 out more and more slowly, and eventually the point is reached where 

 the system is unstable, i.e. the fluctuations no longer are smoothed out: 

 they become cumulative, and even tend to become exaggerated with 

 the passage of time. 



(iii) At this stage the morphogen concentrations form a more or 

 less irregular wave pattern. Later, however (for instance when in some 

 places the concentration of one morphogen is practically zero), the 

 progressive deepening of the waves is arrested. The pattern will then 

 regularise itself, and will eventually reach an equilibrium which is 

 almost perfectly symmetrical. The resulting pattern may be described 

 as a stationary wave. 



Such a stationary wave, in a biological situation, might take the 

 form of the accumulation of one of the morphogens in several, e.g. 

 3, 4, 5 or more, evenly distributed loci on a one-dimensional system such 

 as the circumference of a circle: the other morphogen will tend to 

 accumulate at intermediate loci. 



A patternised distribution of specific metabolites can thus take place 

 in conformity with the laws of physical chemistry as applied to diff'usion- 

 reaction systems; and this will be true whether the morphogenetic 

 substances are held to be specifically gene-determined, or whatever 

 mechanism is assumed to connect such genes with the morphogens. It 

 seems not improbable that reaction systems of the kind indicated in the 

 theory may be of general occurrence in living organisms, but, of 

 course, evidence that this is so is essential. A provisional acceptance 

 of the theory would certainly afford a basis for understanding both 

 the prevalence of homologies of organisation and the diversification 

 of basic kinds of pattern under the impact of genie factors. For, 

 as we have seen, the patternised distribution, or specific location, 

 of metabolites depends on the diffusibility and chemical reaction 

 of the metabolites, some, or many, of which are specifically gene- 

 determined. 



That diff'usion-reaction systems are present in all growing regions, 

 indeed in all living matter, is basic to studies of metabolism. What is 

 novel in Turing's theory is his demonstration that, under suitable 

 conditions, many different diff'usion-reaction systems will eventually 

 give rise to stationary waves; in fact, to a patternised distribution of 



