Figure 1.
From liar paradoxes to Turing patterns. A: ‘The next statement is true. The previous statement is false’ is a zero-dimensional analogue of a stripe-pattern forming system, based on an activator U and inhibitor V (2-D space and 1-D time). Such systems rely on reaction and diffusion to make patterns (local autoactivation, long-range inhibition29,56). B: Rainbow colour coding shows local high expression of activator U (more red) and inhibitor V (more blue). With high autoactivation and weak repression, the activator dominates giving a uniform stability (red). With high transactivation and strong repression, the inhibitor dominates (blue). C: By balancing production, diffusion, reaction and degradation, spots, stripes or waves spontaneously emerge. D: This simulation has the same parameters as (C), except with a lower autocatalysis saturation constant, resulting in spots. E: The discus fish is thought to employ just such a body-patterning mechanism, based on reaction-diffusion. Images and calculations kindly provided by Luciano Marcon and James Sharpe. Discus image by Anka Zolnierzak