CHAPTER 5 Romeo and Juliet, Spontaneous Pattern Formation, and Turing’s Instability

and nerve tremors: Nearly everywhere we find ordered structures and patterns, regularities that arise as if “by themselves”. This “by themselves”: Does it not sound evasive – not-knowing, or not wanting to know? So we ask: How does this “by themselves”, this “self-organization”, work? How can shape and form bring themselves to bear, form and develop themselves from undifferentiated uniformity? How can creation so assert itself and unfold against the omnipresent powers of dissolving, of sinking back into entropic leveling and amorphous homogeneity? And so we may continue asking, astonished and perplexed. Such questions merit a life’s work and are not to be shrugged off with a lecture or a short article. Alan M. Turing (1912–1954) in his work during the year 1952 (see Reference [11]) developed ground-breaking insights into the problem of “self-organization ” or “morphogenesis”, and they still exert a lively influence. This is the same Turing who, aged 26, had laid the foundations for the modern theory of computability and the architecture of computers. During the Second World War he was deeply involved in the deciphering of the German military’s secret ciphe