# 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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