use Plot2D.frink

/** Program to graph an Archimedean spiral in Cartesian coordinates
    from a single equation.

    In polar and parametric form, an Archimedean spiral can be described
    in a few equations:

    r = b theta
    x = r cos[theta]
    y = r sin[theta]

    The challenge here though is to turn those 3 equations in 5 variables
    {x,y,r,b,theta} into a single implicit equation in 3 variables {x,y,b}
    that can be graphed with Frink's interval arithmetic plotting.
       
    This is hard, especially creating equations that cover multiple spirals and
    do not have a lot of divide-by-zero or arctan[y/x] errors where x=0.

    Thanks to Grok for deriving the equations!  I am impressed!
    https://x.com/i/grok/share/pcpdEkE5apACp3RwlnSED4a96
*/

// Simple equation but with lots of divide-by-zeroes
// g = new Plot2D.plot["y/x = tan[sqrt[x^2+y^2]/2]"]

// but a better version without so many divide-by-zero errors is:
//  y cos[sqrt[x^2+y^2]/b] = x sin[sqrt[x^2+y^2]/b]
b = 1/5
g = new Plot2D.plot["y cos[sqrt[x^2+y^2]/(" + inputForm[b] + ")] = x sin[sqrt[x^2+y^2]/(" + inputForm[b] + ")]"]
g.show[]