# How do I fit an equation to this butterfly curve?

I have data which I plotted to visualize. I cant seem to fit any sort of sensible curve to this plot and I wondered how do I approach this task?

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• What have you tried? There are tons of function approximators. Two hints are to use a function $f:\mathbb{R} \mapsto \mathbb{R}^2$ and reflect half of your data. Mar 19 at 4:05
• I've tried exponential,fourier, guassian, polynomial,ect Mar 19 at 4:09
• The plot does not show it but the data points on the sides are sparse Mar 19 at 4:09
• How many terms did you use in the partial Fourier expansion? And what degree of poylnomials? And did you put them into a $f:\mathbb{R} \mapsto \mathbb{R}^2$ vector function? Mar 19 at 4:13
• I'm using matlab and I went through 1-9 in polynomials and 1 to 8 terms in the fourier series. Where can I find these function approximators that take in a real number and put out two real numbers? Mar 19 at 4:17