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The middle wave above could be implemented by implementing a price feed limit at certain ranges of x and increasing the Amplitude value to 0.75 to maintain a peak of 0.5 change.

chart

Rather than a simple sin wave, we could have a sin wave with a period on the way down where the asset would be equal to the backing asset for about a week?

What do you think about the use of Fourier series? https://en.wikipedia.org/wiki/Fourier_series

Think wave interference would be simpler? Combining a triangle/sawtooth wave with a sin wave to get the above desired effect?

Thoughts?