One Attracting Point and One Cycle

One fixed point and one cycle of order seven. The bay corresponding to the fixed point seems to be an infinite ocean in which the cycle bays are islands.

Each bay in the cycle is isolated from others by the fixed point color.

One fixed point and a cycle of order two.

The origin is at the beginning of the spiral.

The attracting cycle in the previous graph is of order eight.

One fixed point and a cycle of order 34.

One attracting fixed point and one cycle of order four. Each of the colors in the cycle have one unbounded bay. The fixed point has four unbounded bays separating the other cycle bays.

One attracting fixed point and one cycle of order five.

One attracting fixed point and one cycle of order 24. The colors of part of the 24-cycle blend into the the fixed point color and seem to fade out.

One attracting fixed point and one cycle of order two.

One attracting fixed point and one cycle of order two. Purple and yellow are the colors in the cycle. The relationship G(sz) = f(G(z)) implies that multiplication by s maps any bay in a cycle onto a bay corresponding to the next color in the cycle. Conversely division by s maps it onto a bay of the previous color in the cycle. Multiplication of a bay by s means expansion by the modulus of s and rotation around the origin by the argument of s.

One attracting fixed point and one cycle of order three. The fixed point color is blue and the cycle colors are orange, a pale green and a brighter green. After repeated multiplications by s, unbounded bays are eventually mapped back onto themselves. Bounded bays are eventually mapped onto bays of the same color and shape (although scaled up in size) but in a different location.