Modelling a monstrous transformation - generalized logistic function fitting.
I'm spitballing a story where the main character goes through a monstrous transformation.
Part of the conceit / my enjoyment is that she's an oncology researcher and will be tracking the transformation over its 18 month duration and trying to understand the chemical and biological processes occurring.
I've semi-arbitrarily decided her starting weight/height (90lbs and 5'6") as well as her end weight/height (1700lbs and ~9’0“). The other aspects of her transformation (teeth, snout, arm length etc) should be irrelevant.
I wanted have the changes follow a general logistic curve, which is a more general version of the Gompertz curve (used in modelling tumor growth).
I've created a spreadsheet where I'd already modelled the transformation with a gaussian function, and figured out (mostly by trial and error) a, b and c values and just added the results at each timestep to make it cumulative... But I realised recently that I can't easily skew that plot.
Part of the reason I wanted it skewed, is that she'll discover a complex negative feedback loop that stops the biological processes from running away and never stopping.
More concretely her height shoots up in the first 6 months, then slows down. Then her weight, that's only slowly been rising, also increases more rapidly before stopping abruptly. That should skew the data points she plots.
I was aiming for her to gain ⅔ of her final height in the first ⅓ of the 18 months, and ⅔ of her final weight in the last ⅓ of her 18 month transformation.
I can almost fit her height this way, but I haven't managed to find the right parameters for her weight. I did so by looking at the starting and final weights, and then using trial and error on the generalised logistic function that's a solution to the Richards's differential equation.
Given my requirements and conditions (start and end points, as well as ⅓ and ⅔ way through points), is there a more reliable way to find the parameters for the generalised logistic function I need to plot, that isn't just trial and error?
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