model includes periodic "pacemakers" and provides "regulation" without ad- 

 ditional assumptions. 



The discussion in ch.6 is likewise based on the notion of wave propagation. 

 The chapter has sections on periodic patterns, on the insect epidermis, on 

 the chick wing bud (with a wave model for epimorphosis) , on imaginal discs 

 and the insect limb (with an interesting elaboration of the "clock-face" 

 model of French et at.), and on retino-tectal projection in amphibians. The 

 author concludes by saying that the notion of static diffusion gradients 

 providing positional information will probably have to be replaced by a com- 

 bination of wave propagation from defined organising centres, and (local or 

 global) "clocks" of some kind which generate spatial and temporal periodici- 

 ties. 



There is much more in the book (particularly in the last chapter) than can 

 be done justice to here. The author aspires after a "balance between know- 

 ledge and vision", and to grasp the significance of this the perusal of the 

 entire book is necessary (even though for the average biologist the going is 

 difficult in places) . 



9. 



G.NICOLIS and I.PRIGOGINE. 1977. SELF-ORGANIZATION IN NONEQUILIBRIUM SYSTEMS; 



from dissipative structures to order through fluctuations 



Wiley, New York, etc. XIV, 491 pp., 124 figs., subject index. £ 20.75 



Contents (abridged): I. The thermodynamic background (4 chs.); II. Mathe- 

 matical aspects of self-organization: deterministic methods (4 chs.); III. 

 Stochastic methods (4 chs.); IV. Control mechanisms in chemical and biol- 

 ogical systems (4 chs.); V. Evolution and population dynamics (2 chs.) 



On reading the word self-organisation every embryologist pricks up his 

 ears. Unfortunately this reviewer lacks all competence in mathematics, and 

 all I can do here is to try and highlight the main features of this book and 

 of its authors' thinking in order to bring them to the attention of develop- 

 mental biologists. (In this notice I will often use or paraphrase the words 

 of the authors without showing this by quotation marks.) 



Most of the striking results of classical thermodynamics refer to equili- 

 brium situations. Later, linear nonequilibrium thermodynamics showed that 

 nonequilibrium may be a source of macroscopic (global) order (the example 

 adduced by the authors is thermal diffusion.) The results of the investiga- 

 tions by Prigogine's group on situations further away from equilibrium, and 

 involving nonlinear equations, can be sketched as follows. When a system 

 (e.g. a chemically reacting mixture described by nonlinear functions of the 

 variables involved) is forced further and further away from equilibrium, the 

 equilibrium solution may become unstable and the system may evolve toward a 

 new type of organisation (a new long-range molecular order) involving coher- 

 ent space-time behaviour (cf . the Benard instability in liquids) . This type 

 of organisation depends on appropriate feedback conditions; the new struc- 

 tures that appear can be maintained only through a sufficient flow of energy 

 and matter and are called "dissipative structures". (Turing's early work 

 concerned one of the first dissipative structures ever studied.) 



The special interest of the biological applications of this approach dis- 

 cussed in the book is brought out by the following quotation,: "While each 

 of the important biomolecules discovered in the recent years is obviously 

 formed according to the laws of physics and chemistry, we have to identify 

 the mechanisms that make the "mass production" of these molecules possible 

 and coordinate their production according to the needs of the organism. It 

 has often been stated that biological organisation requires a series of 

 structures and functions of growing complexity and hierarchial character. 

 One of our main concerns is to understand the way in which transitions be- 

 tween levels occur and to relate the molecular level to the supermolecular 



192 



