Elliptic curve group operator

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Offline gornvix

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« on: December 31, 2017, 07:03:09 PM »
Are there any fractals based on the elliptic curve group operator? By this I mean the group operation rather than simply iterating an elliptic curve formula as has been done already by (1). See (2). I think this operation in R^2 would have to be combined with addition or some form of multiplication in a formula to produce an interesting fractal. A position on the elliptic curve could be stored as a single real number. For a fractal in R^2, x could store one position and y another position. These two positions could be used to find a third position using the group operation. Then another operation could be applied to make for a chaotic map.

(1) https://webbox.lafayette.edu/~reiterc/mvp/ec_julia/index.html
(2) https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication

Linkback: https://fractalforums.org/fractal-mathematics-and-new-theories/28/elliptic-curve-group-operator/667/
« Last Edit: January 02, 2018, 10:51:33 PM by gornvix, Reason: more details »


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