Mystery Curve 2
Tagline for the sequel: “Where the fun is never ending!”
Brent Yorgey was also inspired by John D Cook to write about the Mystery Curve, with some nice insights. When I left my GGB sketch in his comments, he had the great suggestion to parameterize the coefficients. This makes for continuous deformation, as opposed to the dramatic changes of changing the frequency of the exponential. Here it is on GeoGebraTube. Warning: may correlate negatively with productivity.
Jennifer Silverman also had fun with this and made a coloring book, at Anna Hester’s suggestion. The middle two images are Jen’s.
What I’ve found is not that the frequencies matter so much as their ratio. The last two images are different paramenters for a, b, and c in the ratio 1:4:-5. Thinking exponentially, they should just be different by scale.
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