Renormalisation of curlicues

@article{Berry1988RenormalisationOC,
  title={Renormalisation of curlicues},
  author={Michael V Berry and J Goldberg},
  journal={Nonlinearity},
  year={1988},
  volume={1},
  pages={1-26}
}
The recursively spiralling patterns drawn in the complex plane by the values of SL( tau )= Sigma Ln=1 exp(i pi tau n2) as L to infinity with tau fixed in the range 0<or= tau <or=1, depend on the arithmetic of tau . A compendious understanding of the patterns is obtained by iterating an explicit asymptotic renormalisation transformation relating SL( tau ) to a similar sum, magnified by 1/ square root tau and rotated or reflected with a smaller number L tau of terms and a new parameter tau 1( tau… 

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