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Interesting paper here:

https://colala.bcs.rochester.edu/papers/piantadosi2018one.pdf

which using a closed-form solution to the logistic map m(z) = 4z(1−z) of

m

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 closed-form 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: