Butterfly fly curve with points


Can someone help me translate this equation for the butterfly fly curve into grasshopper ?

x = (cos t)(ecos t - 2cos 4t - sin5(t/12))
y = (sin t)(ecos t - 2cos 4t - sin5(t/12))
z = 0

I am imagining that “t” will be replaced with “x” and every empty space will be replaced with “*” multiplication, but that didn’t work out for me.

Here is the original website for the parametric vector equation

240211-Assigment 03 - Movement test 01.3dm (53.4 KB)
240212-Robotic Movement.gh (8.6 KB)

This looks similar but not exactly the same?

butterfly_2024Feb12a.gh (5.8 KB)

x = cos(t) * (exp(cos(t)) - 2*cos(4*t) - pow(sin(t/12),5))
y = sin(t) * (exp(cos(t)) - 2*cos(4*t) - pow(sin(t/12),5))

You have entered the equations for a helix and that’s what is produced.

If you enter these equations (from the site you posted) you will get the result you’re seeking.

butterfly_fly.gh (5.9 KB)

Note: I swapped the equations for x and y to match the orientation from the linked picture.


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Ah yes.

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Funny enough that I deleted the topic after posting it because I found an earlier definition, but am so glad I “undeleted” as your solutions are much better. Thank you :heart_hands: