Butterfly fly curve with points

[Mohanned_Iskanderani]

Hello,

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
https://members.tripod.com/~Paul_Kirby/quantum/param.html

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

[Joseph_Oster]

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))

[kev.r (Kevin)]

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

@Mohanned_Iskanderani

Butterfly curve-011920×802 60 KB

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.

-Kevin

[Joseph_Oster]

@kev.r

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

Ah yes.

[Mohanned_Iskanderani]

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