Butterfly Curve with Python Turtle

Use the following parametric equations to draw a butterfly curve.

x = 100*(math.sin(t)*(math.exp(math.cos(t))-2*math.cos(4*t)-math.sin(t/12)**5))
y = 100*(math.cos(t)*(math.exp(math.cos(t))-2*math.cos(4*t)-math.sin(t/12)**5))

In the equation above t is the parameter of the equations. Let it range from 0 to 12π gradually with small increment.

Butterfly Curve with Python Turtle

Heart with Parametric Equation and Python Turtle

Use the following parametric equations to draw the following filled heart curve.

    x = 10*(16*math.sin(t)**3)
    y = 10*(13*math.cos(t)-5*math.cos(2*t)-2*math.cos(3*t)-math.cos(4*t))

The variable t is the parameter for the curve. Let t range from 0 to 2π with small increment.

Heart Curve with Python Turtle

If you want to draw a simpler heart refer to this tutorial on drawing a simple heart.

Drawing Parametric Curve with Python Turtle

Parametric equations provides a convenient way to draw curves. We will use the following parametric equation in this project.

x = 200*(math.cos(a*t) - math.cos(b*t)**j)
y = 200*(math.sin(c*t) - math.sin(d*t)**k)

In the equations above, t is the parameter. Let is range from 0 to 2π with very small increment. Use different values for a,b,c,d,j,k to draw the following shapes (you can see the their values in the title of the pictures):

4,1,4,1,3,3
80,1,1,80,3,3
80,1,80,1,3,3
9,199,200,9,3,4