This fractal is obtained by iteratively applying the transformation z <- (z*z + r*z*c + c*c)/(z*z + s*z*c + c*c), beginning with z = c and fixing r and s as two conjugate points on the unit circle. The colors are determined by the average value of the iterates as the number of iterations approaches infinity as c is varied over the complex plane. Although the rule used to generate the image is so mathematically simple, the shape is strangely organic and even suggestive of some sort of creature possessing a large head and a barbed tail.