Logo Arts

To New
  # set default screen, pen and turtle values
  ResetAll SetScreenSize [400 400] HideTurtle
  SetSC Black SetPC Green SetPS 1 PenUp
End

To Title
  # write header title and footer equation
  SetPC White
  SetPos [-190 184] Label [Butterfly Curve]
  SetPos [-190 -190]
  Label [e^Cos theta -2*Cos 4*theta +Sin theta/12^5]
End

To DrawCurve
  # draw polar curve
  For [ Theta 0 360 2] [
  SetPos PtoR (56* Curve : Theta ) : Theta
  SetPC Hue 3* : Theta PenDown Wait 1]
End

To PtoR : RadDist : Theta
  # convert polar to rectangular co-ordinates
  LocalMake " X : RadDist *Sin : Theta
  LocalMake " Y : RadDist *Cos : Theta
  Output List : X : Y
End

To Hue : Theta
  # Output RGB hue list from angle :Theta
  Make " Red Round 127.5*(1+Sin : Theta )
  Make " Green Round 127.5*(1+Sin ( : Theta +120))
  Make " Blue Round 127.5*(1+Sin ( : Theta +240))
  Output (List : Red : Green : Blue )
End

To Curve : Theta
  # return distance from origin
  Output (Power 2.7 (Cos : Theta )) -(2*Cos(4* : Theta ))
    +(Power Sin( : Theta /12) 5)
  # Output (1-Abs Minus Sin (6*:Theta)) + 2*Cos (2*:Theta)
  # Output 3*Sqrt Abs Sin 3*:Theta
End

To Go
  New SetPW 2
  Title Draw Curve
End