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Interesting paper here:
https://colala.bcs.rochester.edu/papers/piantadosi2018one.pdf
which using a closedform solution to the logistic map m(z) = 4z(1−z) of
m^{k} (θ) = sin^{2} [ 2^{k} arcsin √ θ]
with a finely tuned parameter θ (extending to hundreds of decimal places) can fit just about any 2 dimensional shape such as:
https://colala.bcs.rochester.edu/papers/piantadosi2018one.pdf
which using a closedform solution to the logistic map m(z) = 4z(1−z) of
m^{k} (θ) = sin^{2} [ 2^{k} arcsin √ θ]
with a finely tuned parameter θ (extending to hundreds of decimal places) can fit just about any 2 dimensional shape such as:
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