External Ray - Images

Images

Dynamic rays

• Julia set for with 2 external ray landing on repelling fixed point alpha

• Julia set and 3 external rays landing on fixed point

• Dynamic external rays landing on repelling period 3 cycle and 3 internal rays landing on fixed point

• Julia set with external rays landing on period 3 orbit

Mandelbrot set for complex quadratic polynomial with parameter rays of root points

• External rays for angles of the form : n / ( 21 - 1) (0/1; 1/1) landing on the point c= 1/4, which is cusp of main cardioid ( period 1 component)

• External rays for angles of the form : n / ( 22 - 1) (1/3, 2/3) landing on the point c= - 3/4, which is root point of period 2 component

• External rays for angles of the form : n / ( 23 - 1) (1/7,2/7) (3/7,4/7) landing on the point c= -1.75 = -7/4 (5/7,6/7) landing on the root points of period 3 components.

• External rays for angles of form : n / ( 24 - 1) (1/15,2/15) (3/15, 4/15) (6/15, 9/15) landing on the root point c= -5/4 (7/15, 8/15) (11/15,12/15) (13/15, 14/15) landing on the root points of period 4 components.

• External rays for angles of form : n / ( 25 - 1) landing on the root points of period 5 components

Parameter space of the complex exponential family f(z)=exp(z)+c. Eight parameter rays landing at this parameter are drawn in black.