My kids and I just put together a spirograph playground. The images that follow are mostly based on their choices for major/minor radii and point offsets.

Code:

struct SpirographGenerator : Generator {
    
    var pointOffset, dTheta, dR, minorRadius, majorRadius : Double    
    var theta = 0.0
    typealias Element = CGPoint
    
    init(majorRadius : Double, minorRadius : Double, pointOffset : Double, samples : Double)
    {
        self.pointOffset = pointOffset
        self.dTheta = Double(M_PI) * (2.0) / samples
        self.majorRadius = majorRadius
        self.minorRadius = minorRadius
        self.dR = majorRadius - minorRadius
    }
    
    mutating func next() -> CGPoint? {
        var xT : Double = dR * cos(theta) + pointOffset * cos(dR * theta / minorRadius)
        var yT : Double = dR * sin(theta) + pointOffset * sin (dR * theta / minorRadius)
        theta = theta + dTheta
        return CGPoint(x: xT, y: yT)
    }
}