Critical waves and the length problem of biology
why pure reaction–diffusion ideas do not produce a satisfactory explanation of biological growth and form.
Two ideas have been missing. One is that oscillation is necessary to achieve the necessary design stability and plasticity. The other is that the system must be tuned to criticality to stabilize the propagation velocity, thus enabling clocks to function as meter sticks. The larger significance is twofold: First, a fundamental piece of the machinery of life is probably invisible to present-day biochemical methods because they are too slow. Second, the simplicity of growth and form identified a century ago by D’Arcy Thompson is probably a symptom of biological engineering strategies, not primitive law.
It is not known how living things measure their lengths. This is true notwithstanding the immense progress made over the past 30 y in understanding morphogen gradients in embryogenesis
No one knows why cells are the size they are (14), why plants and animals are the size they are (15), how organs grow maintaining their proportions (16), and how some animal bodies regenerate lost limbs (17).
Anything one says about eukaryotic size and shape control is necessarily speculative because so little definitive is known about it.
Common Design 