“Floral Table”: A Mapping of the Function z → z⁴ − z + c in the Complex z Plane

The circular pattern in Fig. 1 illustrates a mapping of the polynomial f_c(z) = z⁴ − z + c in the complex z plane for which the divergent points in the z plane iteration of z + c were identified by the iteration value for which |z| < 2. This definition of the escape radius implemented by Mandelbrot [1] determines that the curve for iteration value k = 1 is a circle. Alternative tests for divergence of points in similar mappings have been used [2]. All the points in the bounded set were iterated to a limit of 150…