The butterfly curve
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I came across the butterfly curve, which was discovered by Temple Fay. The butterfly curve is produced by a parametric equation where:
x = sin(t) * (e^cos(t)-2cos(λt)-sin(t/12)^5)
and
y = cos(t) * (e^cos(t)-2cos(λt)-sin(t/12)^5)
.
Where t
stands for time
and λ
for a user input variable.
I used ggplot to create a plot of the butterfly curve with a background of the same color pattern. After sourcing the function, the user can vary the number of background points, as well as the butterfly curves.
library(ggplot2) source("https://raw.githubusercontent.com/danielmarcelino/SciencesPo/master/R/butterfly.R") > p1 = butterfly(10, 100, title="10 x 100") Date of Analysis: Wed Oct 07 2015 Computation time: 0.009749889 ----------------------------------- > p2 = butterfly(10, 200, title="10 x 200") Date of Analysis: Wed Oct 07 2015 Computation time: 0.01240611 ----------------------------------- > p3 = butterfly(10, 500, title="100 x 500") Date of Analysis: Wed Oct 07 2015 Computation time: 0.02488399 ----------------------------------- > p4 = butterfly(100, 1000, title="100 x 1000") Date of Analysis: Wed Oct 07 2015 Computation time: 0.01444697 ----------------------------------- multiplot(p1,p2,p3,p4, ncols = 2)
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