I'm currently taking Andrew Ng's Machine Learning course on Coursera; I immediately thought of using logistic regression to find this shape algorithmically. I

I'm currently taking Andrew Ng's Machine Learning course on Coursera; I immediately thought of using logistic regression to find this shape algorithmically. I know the premise of the paper is "with four parameters." But: with enough polynomial terms it should be easy to get much closer to the example in figure a than the one shown in figure b, no?