Butterfly Curve

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Red Blob

This curve is a polar plot which looks like a butterfly. The equation gives the distance from the origin (R) for angle theta. This one is of the form:
e^Cos theta -2*Cos 4*theta +Sin theta/12^5
Where e is the value 2.718 and theta ranges from 0 to 360 degrees.

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

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]

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

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

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)

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

To Go
  New SetPW 2
  Title Draw Curve

Butterfly Curve
Butterfly Curve

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